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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math.linear;<a name="line.18"></a>
<FONT color="green">019</FONT>    import java.io.Serializable;<a name="line.19"></a>
<FONT color="green">020</FONT>    import java.math.BigDecimal;<a name="line.20"></a>
<FONT color="green">021</FONT>    <a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math.MathRuntimeException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math.exception.util.LocalizedFormats;<a name="line.23"></a>
<FONT color="green">024</FONT>    <a name="line.24"></a>
<FONT color="green">025</FONT>    /**<a name="line.25"></a>
<FONT color="green">026</FONT>     * Implementation of {@link BigMatrix} using a BigDecimal[][] array to store entries<a name="line.26"></a>
<FONT color="green">027</FONT>     * and &lt;a href="http://www.math.gatech.edu/~bourbaki/math2601/Web-notes/2num.pdf"&gt;<a name="line.27"></a>
<FONT color="green">028</FONT>     * LU decompostion&lt;/a&gt; to support linear system<a name="line.28"></a>
<FONT color="green">029</FONT>     * solution and inverse.<a name="line.29"></a>
<FONT color="green">030</FONT>     * &lt;p&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     * The LU decompostion is performed as needed, to support the following operations: &lt;ul&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * &lt;li&gt;solve&lt;/li&gt;<a name="line.32"></a>
<FONT color="green">033</FONT>     * &lt;li&gt;isSingular&lt;/li&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     * &lt;li&gt;getDeterminant&lt;/li&gt;<a name="line.34"></a>
<FONT color="green">035</FONT>     * &lt;li&gt;inverse&lt;/li&gt; &lt;/ul&gt;&lt;/p&gt;<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;p&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>    * &lt;strong&gt;Usage notes&lt;/strong&gt;:&lt;br&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     * &lt;ul&gt;&lt;li&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     * The LU decomposition is stored and reused on subsequent calls.  If matrix<a name="line.39"></a>
<FONT color="green">040</FONT>     * data are modified using any of the public setXxx methods, the saved<a name="line.40"></a>
<FONT color="green">041</FONT>     * decomposition is discarded.  If data are modified via references to the<a name="line.41"></a>
<FONT color="green">042</FONT>     * underlying array obtained using &lt;code&gt;getDataRef()&lt;/code&gt;, then the stored<a name="line.42"></a>
<FONT color="green">043</FONT>     * LU decomposition will not be discarded.  In this case, you need to<a name="line.43"></a>
<FONT color="green">044</FONT>     * explicitly invoke &lt;code&gt;LUDecompose()&lt;/code&gt; to recompute the decomposition<a name="line.44"></a>
<FONT color="green">045</FONT>     * before using any of the methods above.&lt;/li&gt;<a name="line.45"></a>
<FONT color="green">046</FONT>     * &lt;li&gt;<a name="line.46"></a>
<FONT color="green">047</FONT>     * As specified in the {@link BigMatrix} interface, matrix element indexing<a name="line.47"></a>
<FONT color="green">048</FONT>     * is 0-based -- e.g., &lt;code&gt;getEntry(0, 0)&lt;/code&gt;<a name="line.48"></a>
<FONT color="green">049</FONT>     * returns the element in the first row, first column of the matrix.&lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;<a name="line.49"></a>
<FONT color="green">050</FONT>     *<a name="line.50"></a>
<FONT color="green">051</FONT>     * @deprecated as of 2.0, replaced by {@link Array2DRowFieldMatrix} with a {@link<a name="line.51"></a>
<FONT color="green">052</FONT>     * org.apache.commons.math.util.BigReal} parameter<a name="line.52"></a>
<FONT color="green">053</FONT>     * @version $Revision: 1042376 $ $Date: 2010-12-05 16:54:55 +0100 (dim. 05 d??c. 2010) $<a name="line.53"></a>
<FONT color="green">054</FONT>     */<a name="line.54"></a>
<FONT color="green">055</FONT>    @Deprecated<a name="line.55"></a>
<FONT color="green">056</FONT>    public class BigMatrixImpl implements BigMatrix, Serializable {<a name="line.56"></a>
<FONT color="green">057</FONT>    <a name="line.57"></a>
<FONT color="green">058</FONT>        /** BigDecimal 0 */<a name="line.58"></a>
<FONT color="green">059</FONT>        static final BigDecimal ZERO = new BigDecimal(0);<a name="line.59"></a>
<FONT color="green">060</FONT>    <a name="line.60"></a>
<FONT color="green">061</FONT>        /** BigDecimal 1 */<a name="line.61"></a>
<FONT color="green">062</FONT>        static final BigDecimal ONE = new BigDecimal(1);<a name="line.62"></a>
<FONT color="green">063</FONT>    <a name="line.63"></a>
<FONT color="green">064</FONT>        /** Bound to determine effective singularity in LU decomposition */<a name="line.64"></a>
<FONT color="green">065</FONT>        private static final BigDecimal TOO_SMALL = new BigDecimal(10E-12);<a name="line.65"></a>
<FONT color="green">066</FONT>    <a name="line.66"></a>
<FONT color="green">067</FONT>        /** Serialization id */<a name="line.67"></a>
<FONT color="green">068</FONT>        private static final long serialVersionUID = -1011428905656140431L;<a name="line.68"></a>
<FONT color="green">069</FONT>    <a name="line.69"></a>
<FONT color="green">070</FONT>        /** Entries of the matrix */<a name="line.70"></a>
<FONT color="green">071</FONT>        protected BigDecimal data[][] = null;<a name="line.71"></a>
<FONT color="green">072</FONT>    <a name="line.72"></a>
<FONT color="green">073</FONT>        /** Entries of cached LU decomposition.<a name="line.73"></a>
<FONT color="green">074</FONT>         *  All updates to data (other than luDecompose()) *must* set this to null<a name="line.74"></a>
<FONT color="green">075</FONT>         */<a name="line.75"></a>
<FONT color="green">076</FONT>        protected BigDecimal lu[][] = null;<a name="line.76"></a>
<FONT color="green">077</FONT>    <a name="line.77"></a>
<FONT color="green">078</FONT>        /** Permutation associated with LU decomposition */<a name="line.78"></a>
<FONT color="green">079</FONT>        protected int[] permutation = null;<a name="line.79"></a>
<FONT color="green">080</FONT>    <a name="line.80"></a>
<FONT color="green">081</FONT>        /** Parity of the permutation associated with the LU decomposition */<a name="line.81"></a>
<FONT color="green">082</FONT>        protected int parity = 1;<a name="line.82"></a>
<FONT color="green">083</FONT>    <a name="line.83"></a>
<FONT color="green">084</FONT>        /** Rounding mode for divisions **/<a name="line.84"></a>
<FONT color="green">085</FONT>        private int roundingMode = BigDecimal.ROUND_HALF_UP;<a name="line.85"></a>
<FONT color="green">086</FONT>    <a name="line.86"></a>
<FONT color="green">087</FONT>        /*** BigDecimal scale ***/<a name="line.87"></a>
<FONT color="green">088</FONT>        private int scale = 64;<a name="line.88"></a>
<FONT color="green">089</FONT>    <a name="line.89"></a>
<FONT color="green">090</FONT>        /**<a name="line.90"></a>
<FONT color="green">091</FONT>         * Creates a matrix with no data<a name="line.91"></a>
<FONT color="green">092</FONT>         */<a name="line.92"></a>
<FONT color="green">093</FONT>        public BigMatrixImpl() {<a name="line.93"></a>
<FONT color="green">094</FONT>        }<a name="line.94"></a>
<FONT color="green">095</FONT>    <a name="line.95"></a>
<FONT color="green">096</FONT>        /**<a name="line.96"></a>
<FONT color="green">097</FONT>         * Create a new BigMatrix with the supplied row and column dimensions.<a name="line.97"></a>
<FONT color="green">098</FONT>         *<a name="line.98"></a>
<FONT color="green">099</FONT>         * @param rowDimension      the number of rows in the new matrix<a name="line.99"></a>
<FONT color="green">100</FONT>         * @param columnDimension   the number of columns in the new matrix<a name="line.100"></a>
<FONT color="green">101</FONT>         * @throws IllegalArgumentException if row or column dimension is not<a name="line.101"></a>
<FONT color="green">102</FONT>         *  positive<a name="line.102"></a>
<FONT color="green">103</FONT>         */<a name="line.103"></a>
<FONT color="green">104</FONT>        public BigMatrixImpl(int rowDimension, int columnDimension) {<a name="line.104"></a>
<FONT color="green">105</FONT>            if (rowDimension &lt; 1 ) {<a name="line.105"></a>
<FONT color="green">106</FONT>                throw MathRuntimeException.createIllegalArgumentException(<a name="line.106"></a>
<FONT color="green">107</FONT>                        LocalizedFormats.INSUFFICIENT_DIMENSION, rowDimension, 1);<a name="line.107"></a>
<FONT color="green">108</FONT>            }<a name="line.108"></a>
<FONT color="green">109</FONT>            if (columnDimension &lt; 1) {<a name="line.109"></a>
<FONT color="green">110</FONT>                throw MathRuntimeException.createIllegalArgumentException(<a name="line.110"></a>
<FONT color="green">111</FONT>                        LocalizedFormats.INSUFFICIENT_DIMENSION, columnDimension, 1);<a name="line.111"></a>
<FONT color="green">112</FONT>            }<a name="line.112"></a>
<FONT color="green">113</FONT>            data = new BigDecimal[rowDimension][columnDimension];<a name="line.113"></a>
<FONT color="green">114</FONT>            lu = null;<a name="line.114"></a>
<FONT color="green">115</FONT>        }<a name="line.115"></a>
<FONT color="green">116</FONT>    <a name="line.116"></a>
<FONT color="green">117</FONT>        /**<a name="line.117"></a>
<FONT color="green">118</FONT>         * Create a new BigMatrix using &lt;code&gt;d&lt;/code&gt; as the underlying<a name="line.118"></a>
<FONT color="green">119</FONT>         * data array.<a name="line.119"></a>
<FONT color="green">120</FONT>         * &lt;p&gt;The input array is copied, not referenced. This constructor has<a name="line.120"></a>
<FONT color="green">121</FONT>         * the same effect as calling {@link #BigMatrixImpl(BigDecimal[][], boolean)}<a name="line.121"></a>
<FONT color="green">122</FONT>         * with the second argument set to &lt;code&gt;true&lt;/code&gt;.&lt;/p&gt;<a name="line.122"></a>
<FONT color="green">123</FONT>         *<a name="line.123"></a>
<FONT color="green">124</FONT>         * @param d data for new matrix<a name="line.124"></a>
<FONT color="green">125</FONT>         * @throws IllegalArgumentException if &lt;code&gt;d&lt;/code&gt; is not rectangular<a name="line.125"></a>
<FONT color="green">126</FONT>         *  (not all rows have the same length) or empty<a name="line.126"></a>
<FONT color="green">127</FONT>         * @throws NullPointerException if &lt;code&gt;d&lt;/code&gt; is null<a name="line.127"></a>
<FONT color="green">128</FONT>         */<a name="line.128"></a>
<FONT color="green">129</FONT>        public BigMatrixImpl(BigDecimal[][] d) {<a name="line.129"></a>
<FONT color="green">130</FONT>            this.copyIn(d);<a name="line.130"></a>
<FONT color="green">131</FONT>            lu = null;<a name="line.131"></a>
<FONT color="green">132</FONT>        }<a name="line.132"></a>
<FONT color="green">133</FONT>    <a name="line.133"></a>
<FONT color="green">134</FONT>        /**<a name="line.134"></a>
<FONT color="green">135</FONT>         * Create a new BigMatrix using the input array as the underlying<a name="line.135"></a>
<FONT color="green">136</FONT>         * data array.<a name="line.136"></a>
<FONT color="green">137</FONT>         * &lt;p&gt;If an array is built specially in order to be embedded in a<a name="line.137"></a>
<FONT color="green">138</FONT>         * BigMatrix and not used directly, the &lt;code&gt;copyArray&lt;/code&gt; may be<a name="line.138"></a>
<FONT color="green">139</FONT>         * set to &lt;code&gt;false&lt;/code. This will prevent the copying and improve<a name="line.139"></a>
<FONT color="green">140</FONT>         * performance as no new array will be built and no data will be copied.&lt;/p&gt;<a name="line.140"></a>
<FONT color="green">141</FONT>         * @param d data for new matrix<a name="line.141"></a>
<FONT color="green">142</FONT>         * @param copyArray if true, the input array will be copied, otherwise<a name="line.142"></a>
<FONT color="green">143</FONT>         * it will be referenced<a name="line.143"></a>
<FONT color="green">144</FONT>         * @throws IllegalArgumentException if &lt;code&gt;d&lt;/code&gt; is not rectangular<a name="line.144"></a>
<FONT color="green">145</FONT>         *  (not all rows have the same length) or empty<a name="line.145"></a>
<FONT color="green">146</FONT>         * @throws NullPointerException if &lt;code&gt;d&lt;/code&gt; is null<a name="line.146"></a>
<FONT color="green">147</FONT>         * @see #BigMatrixImpl(BigDecimal[][])<a name="line.147"></a>
<FONT color="green">148</FONT>         */<a name="line.148"></a>
<FONT color="green">149</FONT>        public BigMatrixImpl(BigDecimal[][] d, boolean copyArray) {<a name="line.149"></a>
<FONT color="green">150</FONT>            if (copyArray) {<a name="line.150"></a>
<FONT color="green">151</FONT>                copyIn(d);<a name="line.151"></a>
<FONT color="green">152</FONT>            } else {<a name="line.152"></a>
<FONT color="green">153</FONT>                if (d == null) {<a name="line.153"></a>
<FONT color="green">154</FONT>                    throw new NullPointerException();<a name="line.154"></a>
<FONT color="green">155</FONT>                }<a name="line.155"></a>
<FONT color="green">156</FONT>                final int nRows = d.length;<a name="line.156"></a>
<FONT color="green">157</FONT>                if (nRows == 0) {<a name="line.157"></a>
<FONT color="green">158</FONT>                    throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW);<a name="line.158"></a>
<FONT color="green">159</FONT>                }<a name="line.159"></a>
<FONT color="green">160</FONT>    <a name="line.160"></a>
<FONT color="green">161</FONT>                final int nCols = d[0].length;<a name="line.161"></a>
<FONT color="green">162</FONT>                if (nCols == 0) {<a name="line.162"></a>
<FONT color="green">163</FONT>                    throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN);<a name="line.163"></a>
<FONT color="green">164</FONT>                }<a name="line.164"></a>
<FONT color="green">165</FONT>                for (int r = 1; r &lt; nRows; r++) {<a name="line.165"></a>
<FONT color="green">166</FONT>                    if (d[r].length != nCols) {<a name="line.166"></a>
<FONT color="green">167</FONT>                        throw MathRuntimeException.createIllegalArgumentException(<a name="line.167"></a>
<FONT color="green">168</FONT>                              LocalizedFormats.DIFFERENT_ROWS_LENGTHS,<a name="line.168"></a>
<FONT color="green">169</FONT>                              nCols, d[r].length);<a name="line.169"></a>
<FONT color="green">170</FONT>                    }<a name="line.170"></a>
<FONT color="green">171</FONT>                }<a name="line.171"></a>
<FONT color="green">172</FONT>                data = d;<a name="line.172"></a>
<FONT color="green">173</FONT>            }<a name="line.173"></a>
<FONT color="green">174</FONT>            lu = null;<a name="line.174"></a>
<FONT color="green">175</FONT>        }<a name="line.175"></a>
<FONT color="green">176</FONT>    <a name="line.176"></a>
<FONT color="green">177</FONT>        /**<a name="line.177"></a>
<FONT color="green">178</FONT>         * Create a new BigMatrix using &lt;code&gt;d&lt;/code&gt; as the underlying<a name="line.178"></a>
<FONT color="green">179</FONT>         * data array.<a name="line.179"></a>
<FONT color="green">180</FONT>         * &lt;p&gt;Since the underlying array will hold &lt;code&gt;BigDecimal&lt;/code&gt;<a name="line.180"></a>
<FONT color="green">181</FONT>         * instances, it will be created.&lt;/p&gt;<a name="line.181"></a>
<FONT color="green">182</FONT>         *<a name="line.182"></a>
<FONT color="green">183</FONT>         * @param d data for new matrix<a name="line.183"></a>
<FONT color="green">184</FONT>         * @throws IllegalArgumentException if &lt;code&gt;d&lt;/code&gt; is not rectangular<a name="line.184"></a>
<FONT color="green">185</FONT>         *  (not all rows have the same length) or empty<a name="line.185"></a>
<FONT color="green">186</FONT>         * @throws NullPointerException if &lt;code&gt;d&lt;/code&gt; is null<a name="line.186"></a>
<FONT color="green">187</FONT>         */<a name="line.187"></a>
<FONT color="green">188</FONT>        public BigMatrixImpl(double[][] d) {<a name="line.188"></a>
<FONT color="green">189</FONT>            final int nRows = d.length;<a name="line.189"></a>
<FONT color="green">190</FONT>            if (nRows == 0) {<a name="line.190"></a>
<FONT color="green">191</FONT>                throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW);<a name="line.191"></a>
<FONT color="green">192</FONT>            }<a name="line.192"></a>
<FONT color="green">193</FONT>    <a name="line.193"></a>
<FONT color="green">194</FONT>            final int nCols = d[0].length;<a name="line.194"></a>
<FONT color="green">195</FONT>            if (nCols == 0) {<a name="line.195"></a>
<FONT color="green">196</FONT>                throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN);<a name="line.196"></a>
<FONT color="green">197</FONT>            }<a name="line.197"></a>
<FONT color="green">198</FONT>            for (int row = 1; row &lt; nRows; row++) {<a name="line.198"></a>
<FONT color="green">199</FONT>                if (d[row].length != nCols) {<a name="line.199"></a>
<FONT color="green">200</FONT>                    throw MathRuntimeException.createIllegalArgumentException(<a name="line.200"></a>
<FONT color="green">201</FONT>                          LocalizedFormats.DIFFERENT_ROWS_LENGTHS,<a name="line.201"></a>
<FONT color="green">202</FONT>                          nCols, d[row].length);<a name="line.202"></a>
<FONT color="green">203</FONT>                }<a name="line.203"></a>
<FONT color="green">204</FONT>            }<a name="line.204"></a>
<FONT color="green">205</FONT>            this.copyIn(d);<a name="line.205"></a>
<FONT color="green">206</FONT>            lu = null;<a name="line.206"></a>
<FONT color="green">207</FONT>        }<a name="line.207"></a>
<FONT color="green">208</FONT>    <a name="line.208"></a>
<FONT color="green">209</FONT>        /**<a name="line.209"></a>
<FONT color="green">210</FONT>         * Create a new BigMatrix using the values represented by the strings in<a name="line.210"></a>
<FONT color="green">211</FONT>         * &lt;code&gt;d&lt;/code&gt; as the underlying data array.<a name="line.211"></a>
<FONT color="green">212</FONT>         *<a name="line.212"></a>
<FONT color="green">213</FONT>         * @param d data for new matrix<a name="line.213"></a>
<FONT color="green">214</FONT>         * @throws IllegalArgumentException if &lt;code&gt;d&lt;/code&gt; is not rectangular<a name="line.214"></a>
<FONT color="green">215</FONT>         *  (not all rows have the same length) or empty<a name="line.215"></a>
<FONT color="green">216</FONT>         * @throws NullPointerException if &lt;code&gt;d&lt;/code&gt; is null<a name="line.216"></a>
<FONT color="green">217</FONT>         */<a name="line.217"></a>
<FONT color="green">218</FONT>        public BigMatrixImpl(String[][] d) {<a name="line.218"></a>
<FONT color="green">219</FONT>            final int nRows = d.length;<a name="line.219"></a>
<FONT color="green">220</FONT>            if (nRows == 0) {<a name="line.220"></a>
<FONT color="green">221</FONT>                throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW);<a name="line.221"></a>
<FONT color="green">222</FONT>            }<a name="line.222"></a>
<FONT color="green">223</FONT>    <a name="line.223"></a>
<FONT color="green">224</FONT>            final int nCols = d[0].length;<a name="line.224"></a>
<FONT color="green">225</FONT>            if (nCols == 0) {<a name="line.225"></a>
<FONT color="green">226</FONT>                throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN);<a name="line.226"></a>
<FONT color="green">227</FONT>            }<a name="line.227"></a>
<FONT color="green">228</FONT>            for (int row = 1; row &lt; nRows; row++) {<a name="line.228"></a>
<FONT color="green">229</FONT>                if (d[row].length != nCols) {<a name="line.229"></a>
<FONT color="green">230</FONT>                    throw MathRuntimeException.createIllegalArgumentException(<a name="line.230"></a>
<FONT color="green">231</FONT>                          LocalizedFormats.DIFFERENT_ROWS_LENGTHS,<a name="line.231"></a>
<FONT color="green">232</FONT>                          nCols, d[row].length);<a name="line.232"></a>
<FONT color="green">233</FONT>                }<a name="line.233"></a>
<FONT color="green">234</FONT>            }<a name="line.234"></a>
<FONT color="green">235</FONT>            this.copyIn(d);<a name="line.235"></a>
<FONT color="green">236</FONT>            lu = null;<a name="line.236"></a>
<FONT color="green">237</FONT>        }<a name="line.237"></a>
<FONT color="green">238</FONT>    <a name="line.238"></a>
<FONT color="green">239</FONT>        /**<a name="line.239"></a>
<FONT color="green">240</FONT>         * Create a new (column) BigMatrix using &lt;code&gt;v&lt;/code&gt; as the<a name="line.240"></a>
<FONT color="green">241</FONT>         * data for the unique column of the &lt;code&gt;v.length x 1&lt;/code&gt; matrix<a name="line.241"></a>
<FONT color="green">242</FONT>         * created.<a name="line.242"></a>
<FONT color="green">243</FONT>         * &lt;p&gt;<a name="line.243"></a>
<FONT color="green">244</FONT>         * The input array is copied, not referenced.&lt;/p&gt;<a name="line.244"></a>
<FONT color="green">245</FONT>         *<a name="line.245"></a>
<FONT color="green">246</FONT>         * @param v column vector holding data for new matrix<a name="line.246"></a>
<FONT color="green">247</FONT>         */<a name="line.247"></a>
<FONT color="green">248</FONT>        public BigMatrixImpl(BigDecimal[] v) {<a name="line.248"></a>
<FONT color="green">249</FONT>            final int nRows = v.length;<a name="line.249"></a>
<FONT color="green">250</FONT>            data = new BigDecimal[nRows][1];<a name="line.250"></a>
<FONT color="green">251</FONT>            for (int row = 0; row &lt; nRows; row++) {<a name="line.251"></a>
<FONT color="green">252</FONT>                data[row][0] = v[row];<a name="line.252"></a>
<FONT color="green">253</FONT>            }<a name="line.253"></a>
<FONT color="green">254</FONT>        }<a name="line.254"></a>
<FONT color="green">255</FONT>    <a name="line.255"></a>
<FONT color="green">256</FONT>        /**<a name="line.256"></a>
<FONT color="green">257</FONT>         * Create a new BigMatrix which is a copy of this.<a name="line.257"></a>
<FONT color="green">258</FONT>         *<a name="line.258"></a>
<FONT color="green">259</FONT>         * @return  the cloned matrix<a name="line.259"></a>
<FONT color="green">260</FONT>         */<a name="line.260"></a>
<FONT color="green">261</FONT>        public BigMatrix copy() {<a name="line.261"></a>
<FONT color="green">262</FONT>            return new BigMatrixImpl(this.copyOut(), false);<a name="line.262"></a>
<FONT color="green">263</FONT>        }<a name="line.263"></a>
<FONT color="green">264</FONT>    <a name="line.264"></a>
<FONT color="green">265</FONT>        /**<a name="line.265"></a>
<FONT color="green">266</FONT>         * Compute the sum of this and &lt;code&gt;m&lt;/code&gt;.<a name="line.266"></a>
<FONT color="green">267</FONT>         *<a name="line.267"></a>
<FONT color="green">268</FONT>         * @param m    matrix to be added<a name="line.268"></a>
<FONT color="green">269</FONT>         * @return     this + m<a name="line.269"></a>
<FONT color="green">270</FONT>         * @throws  IllegalArgumentException if m is not the same size as this<a name="line.270"></a>
<FONT color="green">271</FONT>         */<a name="line.271"></a>
<FONT color="green">272</FONT>        public BigMatrix add(BigMatrix m) throws IllegalArgumentException {<a name="line.272"></a>
<FONT color="green">273</FONT>            try {<a name="line.273"></a>
<FONT color="green">274</FONT>                return add((BigMatrixImpl) m);<a name="line.274"></a>
<FONT color="green">275</FONT>            } catch (ClassCastException cce) {<a name="line.275"></a>
<FONT color="green">276</FONT>    <a name="line.276"></a>
<FONT color="green">277</FONT>                // safety check<a name="line.277"></a>
<FONT color="green">278</FONT>                MatrixUtils.checkAdditionCompatible(this, m);<a name="line.278"></a>
<FONT color="green">279</FONT>    <a name="line.279"></a>
<FONT color="green">280</FONT>                final int rowCount    = getRowDimension();<a name="line.280"></a>
<FONT color="green">281</FONT>                final int columnCount = getColumnDimension();<a name="line.281"></a>
<FONT color="green">282</FONT>                final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];<a name="line.282"></a>
<FONT color="green">283</FONT>                for (int row = 0; row &lt; rowCount; row++) {<a name="line.283"></a>
<FONT color="green">284</FONT>                    final BigDecimal[] dataRow    = data[row];<a name="line.284"></a>
<FONT color="green">285</FONT>                    final BigDecimal[] outDataRow = outData[row];<a name="line.285"></a>
<FONT color="green">286</FONT>                    for (int col = 0; col &lt; columnCount; col++) {<a name="line.286"></a>
<FONT color="green">287</FONT>                        outDataRow[col] = dataRow[col].add(m.getEntry(row, col));<a name="line.287"></a>
<FONT color="green">288</FONT>                    }<a name="line.288"></a>
<FONT color="green">289</FONT>                }<a name="line.289"></a>
<FONT color="green">290</FONT>                return new BigMatrixImpl(outData, false);<a name="line.290"></a>
<FONT color="green">291</FONT>            }<a name="line.291"></a>
<FONT color="green">292</FONT>        }<a name="line.292"></a>
<FONT color="green">293</FONT>    <a name="line.293"></a>
<FONT color="green">294</FONT>        /**<a name="line.294"></a>
<FONT color="green">295</FONT>         * Compute the sum of this and &lt;code&gt;m&lt;/code&gt;.<a name="line.295"></a>
<FONT color="green">296</FONT>         *<a name="line.296"></a>
<FONT color="green">297</FONT>         * @param m    matrix to be added<a name="line.297"></a>
<FONT color="green">298</FONT>         * @return     this + m<a name="line.298"></a>
<FONT color="green">299</FONT>         * @throws  IllegalArgumentException if m is not the same size as this<a name="line.299"></a>
<FONT color="green">300</FONT>         */<a name="line.300"></a>
<FONT color="green">301</FONT>        public BigMatrixImpl add(BigMatrixImpl m) throws IllegalArgumentException {<a name="line.301"></a>
<FONT color="green">302</FONT>    <a name="line.302"></a>
<FONT color="green">303</FONT>            // safety check<a name="line.303"></a>
<FONT color="green">304</FONT>            MatrixUtils.checkAdditionCompatible(this, m);<a name="line.304"></a>
<FONT color="green">305</FONT>    <a name="line.305"></a>
<FONT color="green">306</FONT>            final int rowCount    = getRowDimension();<a name="line.306"></a>
<FONT color="green">307</FONT>            final int columnCount = getColumnDimension();<a name="line.307"></a>
<FONT color="green">308</FONT>            final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];<a name="line.308"></a>
<FONT color="green">309</FONT>            for (int row = 0; row &lt; rowCount; row++) {<a name="line.309"></a>
<FONT color="green">310</FONT>                final BigDecimal[] dataRow    = data[row];<a name="line.310"></a>
<FONT color="green">311</FONT>                final BigDecimal[] mRow       = m.data[row];<a name="line.311"></a>
<FONT color="green">312</FONT>                final BigDecimal[] outDataRow = outData[row];<a name="line.312"></a>
<FONT color="green">313</FONT>                for (int col = 0; col &lt; columnCount; col++) {<a name="line.313"></a>
<FONT color="green">314</FONT>                    outDataRow[col] = dataRow[col].add(mRow[col]);<a name="line.314"></a>
<FONT color="green">315</FONT>                }<a name="line.315"></a>
<FONT color="green">316</FONT>            }<a name="line.316"></a>
<FONT color="green">317</FONT>            return new BigMatrixImpl(outData, false);<a name="line.317"></a>
<FONT color="green">318</FONT>        }<a name="line.318"></a>
<FONT color="green">319</FONT>    <a name="line.319"></a>
<FONT color="green">320</FONT>        /**<a name="line.320"></a>
<FONT color="green">321</FONT>         * Compute  this minus &lt;code&gt;m&lt;/code&gt;.<a name="line.321"></a>
<FONT color="green">322</FONT>         *<a name="line.322"></a>
<FONT color="green">323</FONT>         * @param m    matrix to be subtracted<a name="line.323"></a>
<FONT color="green">324</FONT>         * @return     this + m<a name="line.324"></a>
<FONT color="green">325</FONT>         * @throws  IllegalArgumentException if m is not the same size as this<a name="line.325"></a>
<FONT color="green">326</FONT>         */<a name="line.326"></a>
<FONT color="green">327</FONT>        public BigMatrix subtract(BigMatrix m) throws IllegalArgumentException {<a name="line.327"></a>
<FONT color="green">328</FONT>            try {<a name="line.328"></a>
<FONT color="green">329</FONT>                return subtract((BigMatrixImpl) m);<a name="line.329"></a>
<FONT color="green">330</FONT>            } catch (ClassCastException cce) {<a name="line.330"></a>
<FONT color="green">331</FONT>    <a name="line.331"></a>
<FONT color="green">332</FONT>                // safety check<a name="line.332"></a>
<FONT color="green">333</FONT>                MatrixUtils.checkSubtractionCompatible(this, m);<a name="line.333"></a>
<FONT color="green">334</FONT>    <a name="line.334"></a>
<FONT color="green">335</FONT>                final int rowCount    = getRowDimension();<a name="line.335"></a>
<FONT color="green">336</FONT>                final int columnCount = getColumnDimension();<a name="line.336"></a>
<FONT color="green">337</FONT>                final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];<a name="line.337"></a>
<FONT color="green">338</FONT>                for (int row = 0; row &lt; rowCount; row++) {<a name="line.338"></a>
<FONT color="green">339</FONT>                    final BigDecimal[] dataRow    = data[row];<a name="line.339"></a>
<FONT color="green">340</FONT>                    final BigDecimal[] outDataRow = outData[row];<a name="line.340"></a>
<FONT color="green">341</FONT>                    for (int col = 0; col &lt; columnCount; col++) {<a name="line.341"></a>
<FONT color="green">342</FONT>                        outDataRow[col] = dataRow[col].subtract(getEntry(row, col));<a name="line.342"></a>
<FONT color="green">343</FONT>                    }<a name="line.343"></a>
<FONT color="green">344</FONT>                }<a name="line.344"></a>
<FONT color="green">345</FONT>                return new BigMatrixImpl(outData, false);<a name="line.345"></a>
<FONT color="green">346</FONT>            }<a name="line.346"></a>
<FONT color="green">347</FONT>        }<a name="line.347"></a>
<FONT color="green">348</FONT>    <a name="line.348"></a>
<FONT color="green">349</FONT>        /**<a name="line.349"></a>
<FONT color="green">350</FONT>         * Compute  this minus &lt;code&gt;m&lt;/code&gt;.<a name="line.350"></a>
<FONT color="green">351</FONT>         *<a name="line.351"></a>
<FONT color="green">352</FONT>         * @param m    matrix to be subtracted<a name="line.352"></a>
<FONT color="green">353</FONT>         * @return     this + m<a name="line.353"></a>
<FONT color="green">354</FONT>         * @throws  IllegalArgumentException if m is not the same size as this<a name="line.354"></a>
<FONT color="green">355</FONT>         */<a name="line.355"></a>
<FONT color="green">356</FONT>        public BigMatrixImpl subtract(BigMatrixImpl m) throws IllegalArgumentException {<a name="line.356"></a>
<FONT color="green">357</FONT>    <a name="line.357"></a>
<FONT color="green">358</FONT>            // safety check<a name="line.358"></a>
<FONT color="green">359</FONT>            MatrixUtils.checkSubtractionCompatible(this, m);<a name="line.359"></a>
<FONT color="green">360</FONT>    <a name="line.360"></a>
<FONT color="green">361</FONT>            final int rowCount    = getRowDimension();<a name="line.361"></a>
<FONT color="green">362</FONT>            final int columnCount = getColumnDimension();<a name="line.362"></a>
<FONT color="green">363</FONT>            final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];<a name="line.363"></a>
<FONT color="green">364</FONT>            for (int row = 0; row &lt; rowCount; row++) {<a name="line.364"></a>
<FONT color="green">365</FONT>                final BigDecimal[] dataRow    = data[row];<a name="line.365"></a>
<FONT color="green">366</FONT>                final BigDecimal[] mRow       = m.data[row];<a name="line.366"></a>
<FONT color="green">367</FONT>                final BigDecimal[] outDataRow = outData[row];<a name="line.367"></a>
<FONT color="green">368</FONT>                for (int col = 0; col &lt; columnCount; col++) {<a name="line.368"></a>
<FONT color="green">369</FONT>                    outDataRow[col] = dataRow[col].subtract(mRow[col]);<a name="line.369"></a>
<FONT color="green">370</FONT>                }<a name="line.370"></a>
<FONT color="green">371</FONT>            }<a name="line.371"></a>
<FONT color="green">372</FONT>            return new BigMatrixImpl(outData, false);<a name="line.372"></a>
<FONT color="green">373</FONT>        }<a name="line.373"></a>
<FONT color="green">374</FONT>    <a name="line.374"></a>
<FONT color="green">375</FONT>        /**<a name="line.375"></a>
<FONT color="green">376</FONT>         * Returns the result of adding d to each entry of this.<a name="line.376"></a>
<FONT color="green">377</FONT>         *<a name="line.377"></a>
<FONT color="green">378</FONT>         * @param d    value to be added to each entry<a name="line.378"></a>
<FONT color="green">379</FONT>         * @return     d + this<a name="line.379"></a>
<FONT color="green">380</FONT>         */<a name="line.380"></a>
<FONT color="green">381</FONT>        public BigMatrix scalarAdd(BigDecimal d) {<a name="line.381"></a>
<FONT color="green">382</FONT>            final int rowCount    = getRowDimension();<a name="line.382"></a>
<FONT color="green">383</FONT>            final int columnCount = getColumnDimension();<a name="line.383"></a>
<FONT color="green">384</FONT>            final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];<a name="line.384"></a>
<FONT color="green">385</FONT>            for (int row = 0; row &lt; rowCount; row++) {<a name="line.385"></a>
<FONT color="green">386</FONT>                final BigDecimal[] dataRow    = data[row];<a name="line.386"></a>
<FONT color="green">387</FONT>                final BigDecimal[] outDataRow = outData[row];<a name="line.387"></a>
<FONT color="green">388</FONT>                for (int col = 0; col &lt; columnCount; col++) {<a name="line.388"></a>
<FONT color="green">389</FONT>                    outDataRow[col] = dataRow[col].add(d);<a name="line.389"></a>
<FONT color="green">390</FONT>                }<a name="line.390"></a>
<FONT color="green">391</FONT>            }<a name="line.391"></a>
<FONT color="green">392</FONT>            return new BigMatrixImpl(outData, false);<a name="line.392"></a>
<FONT color="green">393</FONT>        }<a name="line.393"></a>
<FONT color="green">394</FONT>    <a name="line.394"></a>
<FONT color="green">395</FONT>        /**<a name="line.395"></a>
<FONT color="green">396</FONT>         * Returns the result of multiplying each entry of this by &lt;code&gt;d&lt;/code&gt;<a name="line.396"></a>
<FONT color="green">397</FONT>         * @param d  value to multiply all entries by<a name="line.397"></a>
<FONT color="green">398</FONT>         * @return d * this<a name="line.398"></a>
<FONT color="green">399</FONT>         */<a name="line.399"></a>
<FONT color="green">400</FONT>        public BigMatrix scalarMultiply(BigDecimal d) {<a name="line.400"></a>
<FONT color="green">401</FONT>            final int rowCount    = getRowDimension();<a name="line.401"></a>
<FONT color="green">402</FONT>            final int columnCount = getColumnDimension();<a name="line.402"></a>
<FONT color="green">403</FONT>            final BigDecimal[][] outData = new BigDecimal[rowCount][columnCount];<a name="line.403"></a>
<FONT color="green">404</FONT>            for (int row = 0; row &lt; rowCount; row++) {<a name="line.404"></a>
<FONT color="green">405</FONT>                final BigDecimal[] dataRow    = data[row];<a name="line.405"></a>
<FONT color="green">406</FONT>                final BigDecimal[] outDataRow = outData[row];<a name="line.406"></a>
<FONT color="green">407</FONT>                for (int col = 0; col &lt; columnCount; col++) {<a name="line.407"></a>
<FONT color="green">408</FONT>                    outDataRow[col] = dataRow[col].multiply(d);<a name="line.408"></a>
<FONT color="green">409</FONT>                }<a name="line.409"></a>
<FONT color="green">410</FONT>            }<a name="line.410"></a>
<FONT color="green">411</FONT>            return new BigMatrixImpl(outData, false);<a name="line.411"></a>
<FONT color="green">412</FONT>        }<a name="line.412"></a>
<FONT color="green">413</FONT>    <a name="line.413"></a>
<FONT color="green">414</FONT>        /**<a name="line.414"></a>
<FONT color="green">415</FONT>         * Returns the result of postmultiplying this by &lt;code&gt;m&lt;/code&gt;.<a name="line.415"></a>
<FONT color="green">416</FONT>         * @param m    matrix to postmultiply by<a name="line.416"></a>
<FONT color="green">417</FONT>         * @return     this*m<a name="line.417"></a>
<FONT color="green">418</FONT>         * @throws     IllegalArgumentException<a name="line.418"></a>
<FONT color="green">419</FONT>         *             if columnDimension(this) != rowDimension(m)<a name="line.419"></a>
<FONT color="green">420</FONT>         */<a name="line.420"></a>
<FONT color="green">421</FONT>        public BigMatrix multiply(BigMatrix m) throws IllegalArgumentException {<a name="line.421"></a>
<FONT color="green">422</FONT>            try {<a name="line.422"></a>
<FONT color="green">423</FONT>                return multiply((BigMatrixImpl) m);<a name="line.423"></a>
<FONT color="green">424</FONT>            } catch (ClassCastException cce) {<a name="line.424"></a>
<FONT color="green">425</FONT>    <a name="line.425"></a>
<FONT color="green">426</FONT>                // safety check<a name="line.426"></a>
<FONT color="green">427</FONT>                MatrixUtils.checkMultiplicationCompatible(this, m);<a name="line.427"></a>
<FONT color="green">428</FONT>    <a name="line.428"></a>
<FONT color="green">429</FONT>                final int nRows = this.getRowDimension();<a name="line.429"></a>
<FONT color="green">430</FONT>                final int nCols = m.getColumnDimension();<a name="line.430"></a>
<FONT color="green">431</FONT>                final int nSum = this.getColumnDimension();<a name="line.431"></a>
<FONT color="green">432</FONT>                final BigDecimal[][] outData = new BigDecimal[nRows][nCols];<a name="line.432"></a>
<FONT color="green">433</FONT>                for (int row = 0; row &lt; nRows; row++) {<a name="line.433"></a>
<FONT color="green">434</FONT>                    final BigDecimal[] dataRow    = data[row];<a name="line.434"></a>
<FONT color="green">435</FONT>                    final BigDecimal[] outDataRow = outData[row];<a name="line.435"></a>
<FONT color="green">436</FONT>                    for (int col = 0; col &lt; nCols; col++) {<a name="line.436"></a>
<FONT color="green">437</FONT>                        BigDecimal sum = ZERO;<a name="line.437"></a>
<FONT color="green">438</FONT>                        for (int i = 0; i &lt; nSum; i++) {<a name="line.438"></a>
<FONT color="green">439</FONT>                            sum = sum.add(dataRow[i].multiply(m.getEntry(i, col)));<a name="line.439"></a>
<FONT color="green">440</FONT>                        }<a name="line.440"></a>
<FONT color="green">441</FONT>                        outDataRow[col] = sum;<a name="line.441"></a>
<FONT color="green">442</FONT>                    }<a name="line.442"></a>
<FONT color="green">443</FONT>                }<a name="line.443"></a>
<FONT color="green">444</FONT>                return new BigMatrixImpl(outData, false);<a name="line.444"></a>
<FONT color="green">445</FONT>            }<a name="line.445"></a>
<FONT color="green">446</FONT>        }<a name="line.446"></a>
<FONT color="green">447</FONT>    <a name="line.447"></a>
<FONT color="green">448</FONT>        /**<a name="line.448"></a>
<FONT color="green">449</FONT>         * Returns the result of postmultiplying this by &lt;code&gt;m&lt;/code&gt;.<a name="line.449"></a>
<FONT color="green">450</FONT>         * @param m    matrix to postmultiply by<a name="line.450"></a>
<FONT color="green">451</FONT>         * @return     this*m<a name="line.451"></a>
<FONT color="green">452</FONT>         * @throws     IllegalArgumentException<a name="line.452"></a>
<FONT color="green">453</FONT>         *             if columnDimension(this) != rowDimension(m)<a name="line.453"></a>
<FONT color="green">454</FONT>         */<a name="line.454"></a>
<FONT color="green">455</FONT>        public BigMatrixImpl multiply(BigMatrixImpl m) throws IllegalArgumentException {<a name="line.455"></a>
<FONT color="green">456</FONT>    <a name="line.456"></a>
<FONT color="green">457</FONT>            // safety check<a name="line.457"></a>
<FONT color="green">458</FONT>            MatrixUtils.checkMultiplicationCompatible(this, m);<a name="line.458"></a>
<FONT color="green">459</FONT>    <a name="line.459"></a>
<FONT color="green">460</FONT>            final int nRows = this.getRowDimension();<a name="line.460"></a>
<FONT color="green">461</FONT>            final int nCols = m.getColumnDimension();<a name="line.461"></a>
<FONT color="green">462</FONT>            final int nSum = this.getColumnDimension();<a name="line.462"></a>
<FONT color="green">463</FONT>            final BigDecimal[][] outData = new BigDecimal[nRows][nCols];<a name="line.463"></a>
<FONT color="green">464</FONT>            for (int row = 0; row &lt; nRows; row++) {<a name="line.464"></a>
<FONT color="green">465</FONT>                final BigDecimal[] dataRow    = data[row];<a name="line.465"></a>
<FONT color="green">466</FONT>                final BigDecimal[] outDataRow = outData[row];<a name="line.466"></a>
<FONT color="green">467</FONT>                for (int col = 0; col &lt; nCols; col++) {<a name="line.467"></a>
<FONT color="green">468</FONT>                    BigDecimal sum = ZERO;<a name="line.468"></a>
<FONT color="green">469</FONT>                    for (int i = 0; i &lt; nSum; i++) {<a name="line.469"></a>
<FONT color="green">470</FONT>                        sum = sum.add(dataRow[i].multiply(m.data[i][col]));<a name="line.470"></a>
<FONT color="green">471</FONT>                    }<a name="line.471"></a>
<FONT color="green">472</FONT>                    outDataRow[col] = sum;<a name="line.472"></a>
<FONT color="green">473</FONT>                }<a name="line.473"></a>
<FONT color="green">474</FONT>            }<a name="line.474"></a>
<FONT color="green">475</FONT>            return new BigMatrixImpl(outData, false);<a name="line.475"></a>
<FONT color="green">476</FONT>        }<a name="line.476"></a>
<FONT color="green">477</FONT>    <a name="line.477"></a>
<FONT color="green">478</FONT>        /**<a name="line.478"></a>
<FONT color="green">479</FONT>         * Returns the result premultiplying this by &lt;code&gt;m&lt;/code&gt;.<a name="line.479"></a>
<FONT color="green">480</FONT>         * @param m    matrix to premultiply by<a name="line.480"></a>
<FONT color="green">481</FONT>         * @return     m * this<a name="line.481"></a>
<FONT color="green">482</FONT>         * @throws     IllegalArgumentException<a name="line.482"></a>
<FONT color="green">483</FONT>         *             if rowDimension(this) != columnDimension(m)<a name="line.483"></a>
<FONT color="green">484</FONT>         */<a name="line.484"></a>
<FONT color="green">485</FONT>        public BigMatrix preMultiply(BigMatrix m) throws IllegalArgumentException {<a name="line.485"></a>
<FONT color="green">486</FONT>            return m.multiply(this);<a name="line.486"></a>
<FONT color="green">487</FONT>        }<a name="line.487"></a>
<FONT color="green">488</FONT>    <a name="line.488"></a>
<FONT color="green">489</FONT>        /**<a name="line.489"></a>
<FONT color="green">490</FONT>         * Returns matrix entries as a two-dimensional array.<a name="line.490"></a>
<FONT color="green">491</FONT>         * &lt;p&gt;<a name="line.491"></a>
<FONT color="green">492</FONT>         * Makes a fresh copy of the underlying data.&lt;/p&gt;<a name="line.492"></a>
<FONT color="green">493</FONT>         *<a name="line.493"></a>
<FONT color="green">494</FONT>         * @return    2-dimensional array of entries<a name="line.494"></a>
<FONT color="green">495</FONT>         */<a name="line.495"></a>
<FONT color="green">496</FONT>        public BigDecimal[][] getData() {<a name="line.496"></a>
<FONT color="green">497</FONT>            return copyOut();<a name="line.497"></a>
<FONT color="green">498</FONT>        }<a name="line.498"></a>
<FONT color="green">499</FONT>    <a name="line.499"></a>
<FONT color="green">500</FONT>        /**<a name="line.500"></a>
<FONT color="green">501</FONT>         * Returns matrix entries as a two-dimensional array.<a name="line.501"></a>
<FONT color="green">502</FONT>         * &lt;p&gt;<a name="line.502"></a>
<FONT color="green">503</FONT>         * Makes a fresh copy of the underlying data converted to<a name="line.503"></a>
<FONT color="green">504</FONT>         * &lt;code&gt;double&lt;/code&gt; values.&lt;/p&gt;<a name="line.504"></a>
<FONT color="green">505</FONT>         *<a name="line.505"></a>
<FONT color="green">506</FONT>         * @return    2-dimensional array of entries<a name="line.506"></a>
<FONT color="green">507</FONT>         */<a name="line.507"></a>
<FONT color="green">508</FONT>        public double[][] getDataAsDoubleArray() {<a name="line.508"></a>
<FONT color="green">509</FONT>            final int nRows = getRowDimension();<a name="line.509"></a>
<FONT color="green">510</FONT>            final int nCols = getColumnDimension();<a name="line.510"></a>
<FONT color="green">511</FONT>            final double d[][] = new double[nRows][nCols];<a name="line.511"></a>
<FONT color="green">512</FONT>            for (int i = 0; i &lt; nRows; i++) {<a name="line.512"></a>
<FONT color="green">513</FONT>                for (int j = 0; j &lt; nCols; j++) {<a name="line.513"></a>
<FONT color="green">514</FONT>                    d[i][j] = data[i][j].doubleValue();<a name="line.514"></a>
<FONT color="green">515</FONT>                }<a name="line.515"></a>
<FONT color="green">516</FONT>            }<a name="line.516"></a>
<FONT color="green">517</FONT>            return d;<a name="line.517"></a>
<FONT color="green">518</FONT>        }<a name="line.518"></a>
<FONT color="green">519</FONT>    <a name="line.519"></a>
<FONT color="green">520</FONT>        /**<a name="line.520"></a>
<FONT color="green">521</FONT>         * Returns a reference to the underlying data array.<a name="line.521"></a>
<FONT color="green">522</FONT>         * &lt;p&gt;<a name="line.522"></a>
<FONT color="green">523</FONT>         * Does not make a fresh copy of the underlying data.&lt;/p&gt;<a name="line.523"></a>
<FONT color="green">524</FONT>         *<a name="line.524"></a>
<FONT color="green">525</FONT>         * @return 2-dimensional array of entries<a name="line.525"></a>
<FONT color="green">526</FONT>         */<a name="line.526"></a>
<FONT color="green">527</FONT>        public BigDecimal[][] getDataRef() {<a name="line.527"></a>
<FONT color="green">528</FONT>            return data;<a name="line.528"></a>
<FONT color="green">529</FONT>        }<a name="line.529"></a>
<FONT color="green">530</FONT>    <a name="line.530"></a>
<FONT color="green">531</FONT>        /***<a name="line.531"></a>
<FONT color="green">532</FONT>         * Gets the rounding mode for division operations<a name="line.532"></a>
<FONT color="green">533</FONT>         * The default is {@link java.math.BigDecimal#ROUND_HALF_UP}<a name="line.533"></a>
<FONT color="green">534</FONT>         * @see BigDecimal<a name="line.534"></a>
<FONT color="green">535</FONT>         * @return the rounding mode.<a name="line.535"></a>
<FONT color="green">536</FONT>         */<a name="line.536"></a>
<FONT color="green">537</FONT>        public int getRoundingMode() {<a name="line.537"></a>
<FONT color="green">538</FONT>            return roundingMode;<a name="line.538"></a>
<FONT color="green">539</FONT>        }<a name="line.539"></a>
<FONT color="green">540</FONT>    <a name="line.540"></a>
<FONT color="green">541</FONT>        /***<a name="line.541"></a>
<FONT color="green">542</FONT>         * Sets the rounding mode for decimal divisions.<a name="line.542"></a>
<FONT color="green">543</FONT>         * @see BigDecimal<a name="line.543"></a>
<FONT color="green">544</FONT>         * @param roundingMode rounding mode for decimal divisions<a name="line.544"></a>
<FONT color="green">545</FONT>         */<a name="line.545"></a>
<FONT color="green">546</FONT>        public void setRoundingMode(int roundingMode) {<a name="line.546"></a>
<FONT color="green">547</FONT>            this.roundingMode = roundingMode;<a name="line.547"></a>
<FONT color="green">548</FONT>        }<a name="line.548"></a>
<FONT color="green">549</FONT>    <a name="line.549"></a>
<FONT color="green">550</FONT>        /***<a name="line.550"></a>
<FONT color="green">551</FONT>         * Sets the scale for division operations.<a name="line.551"></a>
<FONT color="green">552</FONT>         * The default is 64<a name="line.552"></a>
<FONT color="green">553</FONT>         * @see BigDecimal<a name="line.553"></a>
<FONT color="green">554</FONT>         * @return the scale<a name="line.554"></a>
<FONT color="green">555</FONT>         */<a name="line.555"></a>
<FONT color="green">556</FONT>        public int getScale() {<a name="line.556"></a>
<FONT color="green">557</FONT>            return scale;<a name="line.557"></a>
<FONT color="green">558</FONT>        }<a name="line.558"></a>
<FONT color="green">559</FONT>    <a name="line.559"></a>
<FONT color="green">560</FONT>        /***<a name="line.560"></a>
<FONT color="green">561</FONT>         * Sets the scale for division operations.<a name="line.561"></a>
<FONT color="green">562</FONT>         * @see BigDecimal<a name="line.562"></a>
<FONT color="green">563</FONT>         * @param scale scale for division operations<a name="line.563"></a>
<FONT color="green">564</FONT>         */<a name="line.564"></a>
<FONT color="green">565</FONT>        public void setScale(int scale) {<a name="line.565"></a>
<FONT color="green">566</FONT>            this.scale = scale;<a name="line.566"></a>
<FONT color="green">567</FONT>        }<a name="line.567"></a>
<FONT color="green">568</FONT>    <a name="line.568"></a>
<FONT color="green">569</FONT>        /**<a name="line.569"></a>
<FONT color="green">570</FONT>         * Returns the &lt;a href="http://mathworld.wolfram.com/MaximumAbsoluteRowSumNorm.html"&gt;<a name="line.570"></a>
<FONT color="green">571</FONT>         * maximum absolute row sum norm&lt;/a&gt; of the matrix.<a name="line.571"></a>
<FONT color="green">572</FONT>         *<a name="line.572"></a>
<FONT color="green">573</FONT>         * @return norm<a name="line.573"></a>
<FONT color="green">574</FONT>         */<a name="line.574"></a>
<FONT color="green">575</FONT>        public BigDecimal getNorm() {<a name="line.575"></a>
<FONT color="green">576</FONT>            BigDecimal maxColSum = ZERO;<a name="line.576"></a>
<FONT color="green">577</FONT>            for (int col = 0; col &lt; this.getColumnDimension(); col++) {<a name="line.577"></a>
<FONT color="green">578</FONT>                BigDecimal sum = ZERO;<a name="line.578"></a>
<FONT color="green">579</FONT>                for (int row = 0; row &lt; this.getRowDimension(); row++) {<a name="line.579"></a>
<FONT color="green">580</FONT>                    sum = sum.add(data[row][col].abs());<a name="line.580"></a>
<FONT color="green">581</FONT>                }<a name="line.581"></a>
<FONT color="green">582</FONT>                maxColSum = maxColSum.max(sum);<a name="line.582"></a>
<FONT color="green">583</FONT>            }<a name="line.583"></a>
<FONT color="green">584</FONT>            return maxColSum;<a name="line.584"></a>
<FONT color="green">585</FONT>        }<a name="line.585"></a>
<FONT color="green">586</FONT>    <a name="line.586"></a>
<FONT color="green">587</FONT>        /**<a name="line.587"></a>
<FONT color="green">588</FONT>         * Gets a submatrix. Rows and columns are indicated<a name="line.588"></a>
<FONT color="green">589</FONT>         * counting from 0 to n-1.<a name="line.589"></a>
<FONT color="green">590</FONT>         *<a name="line.590"></a>
<FONT color="green">591</FONT>         * @param startRow Initial row index<a name="line.591"></a>
<FONT color="green">592</FONT>         * @param endRow Final row index<a name="line.592"></a>
<FONT color="green">593</FONT>         * @param startColumn Initial column index<a name="line.593"></a>
<FONT color="green">594</FONT>         * @param endColumn Final column index<a name="line.594"></a>
<FONT color="green">595</FONT>         * @return The subMatrix containing the data of the<a name="line.595"></a>
<FONT color="green">596</FONT>         *         specified rows and columns<a name="line.596"></a>
<FONT color="green">597</FONT>         * @exception MatrixIndexException if row or column selections are not valid<a name="line.597"></a>
<FONT color="green">598</FONT>         */<a name="line.598"></a>
<FONT color="green">599</FONT>        public BigMatrix getSubMatrix(int startRow, int endRow,<a name="line.599"></a>
<FONT color="green">600</FONT>                                      int startColumn, int endColumn)<a name="line.600"></a>
<FONT color="green">601</FONT>            throws MatrixIndexException {<a name="line.601"></a>
<FONT color="green">602</FONT>    <a name="line.602"></a>
<FONT color="green">603</FONT>            MatrixUtils.checkRowIndex(this, startRow);<a name="line.603"></a>
<FONT color="green">604</FONT>            MatrixUtils.checkRowIndex(this, endRow);<a name="line.604"></a>
<FONT color="green">605</FONT>            if (startRow &gt; endRow) {<a name="line.605"></a>
<FONT color="green">606</FONT>                throw new MatrixIndexException(LocalizedFormats.INITIAL_ROW_AFTER_FINAL_ROW,<a name="line.606"></a>
<FONT color="green">607</FONT>                                               startRow, endRow);<a name="line.607"></a>
<FONT color="green">608</FONT>            }<a name="line.608"></a>
<FONT color="green">609</FONT>    <a name="line.609"></a>
<FONT color="green">610</FONT>            MatrixUtils.checkColumnIndex(this, startColumn);<a name="line.610"></a>
<FONT color="green">611</FONT>            MatrixUtils.checkColumnIndex(this, endColumn);<a name="line.611"></a>
<FONT color="green">612</FONT>            if (startColumn &gt; endColumn) {<a name="line.612"></a>
<FONT color="green">613</FONT>                throw new MatrixIndexException(LocalizedFormats.INITIAL_COLUMN_AFTER_FINAL_COLUMN,<a name="line.613"></a>
<FONT color="green">614</FONT>                                               startColumn, endColumn);<a name="line.614"></a>
<FONT color="green">615</FONT>            }<a name="line.615"></a>
<FONT color="green">616</FONT>    <a name="line.616"></a>
<FONT color="green">617</FONT>            final BigDecimal[][] subMatrixData =<a name="line.617"></a>
<FONT color="green">618</FONT>                new BigDecimal[endRow - startRow + 1][endColumn - startColumn + 1];<a name="line.618"></a>
<FONT color="green">619</FONT>            for (int i = startRow; i &lt;= endRow; i++) {<a name="line.619"></a>
<FONT color="green">620</FONT>                System.arraycopy(data[i], startColumn,<a name="line.620"></a>
<FONT color="green">621</FONT>                                 subMatrixData[i - startRow], 0,<a name="line.621"></a>
<FONT color="green">622</FONT>                                 endColumn - startColumn + 1);<a name="line.622"></a>
<FONT color="green">623</FONT>            }<a name="line.623"></a>
<FONT color="green">624</FONT>    <a name="line.624"></a>
<FONT color="green">625</FONT>            return new BigMatrixImpl(subMatrixData, false);<a name="line.625"></a>
<FONT color="green">626</FONT>    <a name="line.626"></a>
<FONT color="green">627</FONT>        }<a name="line.627"></a>
<FONT color="green">628</FONT>    <a name="line.628"></a>
<FONT color="green">629</FONT>        /**<a name="line.629"></a>
<FONT color="green">630</FONT>         * Gets a submatrix. Rows and columns are indicated<a name="line.630"></a>
<FONT color="green">631</FONT>         * counting from 0 to n-1.<a name="line.631"></a>
<FONT color="green">632</FONT>         *<a name="line.632"></a>
<FONT color="green">633</FONT>         * @param selectedRows Array of row indices must be non-empty<a name="line.633"></a>
<FONT color="green">634</FONT>         * @param selectedColumns Array of column indices must be non-empty<a name="line.634"></a>
<FONT color="green">635</FONT>         * @return The subMatrix containing the data in the<a name="line.635"></a>
<FONT color="green">636</FONT>         *     specified rows and columns<a name="line.636"></a>
<FONT color="green">637</FONT>         * @exception MatrixIndexException  if supplied row or column index arrays<a name="line.637"></a>
<FONT color="green">638</FONT>         *     are not valid<a name="line.638"></a>
<FONT color="green">639</FONT>         */<a name="line.639"></a>
<FONT color="green">640</FONT>        public BigMatrix getSubMatrix(int[] selectedRows, int[] selectedColumns)<a name="line.640"></a>
<FONT color="green">641</FONT>            throws MatrixIndexException {<a name="line.641"></a>
<FONT color="green">642</FONT>    <a name="line.642"></a>
<FONT color="green">643</FONT>            if (selectedRows.length * selectedColumns.length == 0) {<a name="line.643"></a>
<FONT color="green">644</FONT>                if (selectedRows.length == 0) {<a name="line.644"></a>
<FONT color="green">645</FONT>                    throw new MatrixIndexException(LocalizedFormats.EMPTY_SELECTED_ROW_INDEX_ARRAY);<a name="line.645"></a>
<FONT color="green">646</FONT>                }<a name="line.646"></a>
<FONT color="green">647</FONT>                throw new MatrixIndexException(LocalizedFormats.EMPTY_SELECTED_COLUMN_INDEX_ARRAY);<a name="line.647"></a>
<FONT color="green">648</FONT>            }<a name="line.648"></a>
<FONT color="green">649</FONT>    <a name="line.649"></a>
<FONT color="green">650</FONT>            final BigDecimal[][] subMatrixData =<a name="line.650"></a>
<FONT color="green">651</FONT>                new BigDecimal[selectedRows.length][selectedColumns.length];<a name="line.651"></a>
<FONT color="green">652</FONT>            try  {<a name="line.652"></a>
<FONT color="green">653</FONT>                for (int i = 0; i &lt; selectedRows.length; i++) {<a name="line.653"></a>
<FONT color="green">654</FONT>                    final BigDecimal[] subI = subMatrixData[i];<a name="line.654"></a>
<FONT color="green">655</FONT>                    final BigDecimal[] dataSelectedI = data[selectedRows[i]];<a name="line.655"></a>
<FONT color="green">656</FONT>                    for (int j = 0; j &lt; selectedColumns.length; j++) {<a name="line.656"></a>
<FONT color="green">657</FONT>                        subI[j] = dataSelectedI[selectedColumns[j]];<a name="line.657"></a>
<FONT color="green">658</FONT>                    }<a name="line.658"></a>
<FONT color="green">659</FONT>                }<a name="line.659"></a>
<FONT color="green">660</FONT>            } catch (ArrayIndexOutOfBoundsException e) {<a name="line.660"></a>
<FONT color="green">661</FONT>                // we redo the loop with checks enabled<a name="line.661"></a>
<FONT color="green">662</FONT>                // in order to generate an appropriate message<a name="line.662"></a>
<FONT color="green">663</FONT>                for (final int row : selectedRows) {<a name="line.663"></a>
<FONT color="green">664</FONT>                    MatrixUtils.checkRowIndex(this, row);<a name="line.664"></a>
<FONT color="green">665</FONT>                }<a name="line.665"></a>
<FONT color="green">666</FONT>                for (final int column : selectedColumns) {<a name="line.666"></a>
<FONT color="green">667</FONT>                    MatrixUtils.checkColumnIndex(this, column);<a name="line.667"></a>
<FONT color="green">668</FONT>                }<a name="line.668"></a>
<FONT color="green">669</FONT>            }<a name="line.669"></a>
<FONT color="green">670</FONT>            return new BigMatrixImpl(subMatrixData, false);<a name="line.670"></a>
<FONT color="green">671</FONT>        }<a name="line.671"></a>
<FONT color="green">672</FONT>    <a name="line.672"></a>
<FONT color="green">673</FONT>        /**<a name="line.673"></a>
<FONT color="green">674</FONT>         * Replace the submatrix starting at &lt;code&gt;row, column&lt;/code&gt; using data in<a name="line.674"></a>
<FONT color="green">675</FONT>         * the input &lt;code&gt;subMatrix&lt;/code&gt; array. Indexes are 0-based.<a name="line.675"></a>
<FONT color="green">676</FONT>         * &lt;p&gt;<a name="line.676"></a>
<FONT color="green">677</FONT>         * Example:&lt;br&gt;<a name="line.677"></a>
<FONT color="green">678</FONT>         * Starting with &lt;pre&gt;<a name="line.678"></a>
<FONT color="green">679</FONT>         * 1  2  3  4<a name="line.679"></a>
<FONT color="green">680</FONT>         * 5  6  7  8<a name="line.680"></a>
<FONT color="green">681</FONT>         * 9  0  1  2<a name="line.681"></a>
<FONT color="green">682</FONT>         * &lt;/pre&gt;<a name="line.682"></a>
<FONT color="green">683</FONT>         * and &lt;code&gt;subMatrix = {{3, 4} {5,6}}&lt;/code&gt;, invoking<a name="line.683"></a>
<FONT color="green">684</FONT>         * &lt;code&gt;setSubMatrix(subMatrix,1,1))&lt;/code&gt; will result in &lt;pre&gt;<a name="line.684"></a>
<FONT color="green">685</FONT>         * 1  2  3  4<a name="line.685"></a>
<FONT color="green">686</FONT>         * 5  3  4  8<a name="line.686"></a>
<FONT color="green">687</FONT>         * 9  5  6  2<a name="line.687"></a>
<FONT color="green">688</FONT>         * &lt;/pre&gt;&lt;/p&gt;<a name="line.688"></a>
<FONT color="green">689</FONT>         *<a name="line.689"></a>
<FONT color="green">690</FONT>         * @param subMatrix  array containing the submatrix replacement data<a name="line.690"></a>
<FONT color="green">691</FONT>         * @param row  row coordinate of the top, left element to be replaced<a name="line.691"></a>
<FONT color="green">692</FONT>         * @param column  column coordinate of the top, left element to be replaced<a name="line.692"></a>
<FONT color="green">693</FONT>         * @throws MatrixIndexException  if subMatrix does not fit into this<a name="line.693"></a>
<FONT color="green">694</FONT>         *    matrix from element in (row, column)<a name="line.694"></a>
<FONT color="green">695</FONT>         * @throws IllegalArgumentException if &lt;code&gt;subMatrix&lt;/code&gt; is not rectangular<a name="line.695"></a>
<FONT color="green">696</FONT>         *  (not all rows have the same length) or empty<a name="line.696"></a>
<FONT color="green">697</FONT>         * @throws NullPointerException if &lt;code&gt;subMatrix&lt;/code&gt; is null<a name="line.697"></a>
<FONT color="green">698</FONT>         * @since 1.1<a name="line.698"></a>
<FONT color="green">699</FONT>         */<a name="line.699"></a>
<FONT color="green">700</FONT>        public void setSubMatrix(BigDecimal[][] subMatrix, int row, int column)<a name="line.700"></a>
<FONT color="green">701</FONT>        throws MatrixIndexException {<a name="line.701"></a>
<FONT color="green">702</FONT>    <a name="line.702"></a>
<FONT color="green">703</FONT>            final int nRows = subMatrix.length;<a name="line.703"></a>
<FONT color="green">704</FONT>            if (nRows == 0) {<a name="line.704"></a>
<FONT color="green">705</FONT>                throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_ROW);<a name="line.705"></a>
<FONT color="green">706</FONT>            }<a name="line.706"></a>
<FONT color="green">707</FONT>    <a name="line.707"></a>
<FONT color="green">708</FONT>            final int nCols = subMatrix[0].length;<a name="line.708"></a>
<FONT color="green">709</FONT>            if (nCols == 0) {<a name="line.709"></a>
<FONT color="green">710</FONT>                throw MathRuntimeException.createIllegalArgumentException(LocalizedFormats.AT_LEAST_ONE_COLUMN);<a name="line.710"></a>
<FONT color="green">711</FONT>            }<a name="line.711"></a>
<FONT color="green">712</FONT>    <a name="line.712"></a>
<FONT color="green">713</FONT>            for (int r = 1; r &lt; nRows; r++) {<a name="line.713"></a>
<FONT color="green">714</FONT>                if (subMatrix[r].length != nCols) {<a name="line.714"></a>
<FONT color="green">715</FONT>                    throw MathRuntimeException.createIllegalArgumentException(<a name="line.715"></a>
<FONT color="green">716</FONT>                          LocalizedFormats.DIFFERENT_ROWS_LENGTHS,<a name="line.716"></a>
<FONT color="green">717</FONT>                          nCols, subMatrix[r].length);<a name="line.717"></a>
<FONT color="green">718</FONT>                }<a name="line.718"></a>
<FONT color="green">719</FONT>            }<a name="line.719"></a>
<FONT color="green">720</FONT>    <a name="line.720"></a>
<FONT color="green">721</FONT>            if (data == null) {<a name="line.721"></a>
<FONT color="green">722</FONT>                if (row &gt; 0) {<a name="line.722"></a>
<FONT color="green">723</FONT>                    throw MathRuntimeException.createIllegalStateException(<a name="line.723"></a>
<FONT color="green">724</FONT>                            LocalizedFormats.FIRST_ROWS_NOT_INITIALIZED_YET,<a name="line.724"></a>
<FONT color="green">725</FONT>                            row);<a name="line.725"></a>
<FONT color="green">726</FONT>                }<a name="line.726"></a>
<FONT color="green">727</FONT>                if (column &gt; 0) {<a name="line.727"></a>
<FONT color="green">728</FONT>                    throw MathRuntimeException.createIllegalStateException(<a name="line.728"></a>
<FONT color="green">729</FONT>                            LocalizedFormats.FIRST_COLUMNS_NOT_INITIALIZED_YET,<a name="line.729"></a>
<FONT color="green">730</FONT>                            column);<a name="line.730"></a>
<FONT color="green">731</FONT>                }<a name="line.731"></a>
<FONT color="green">732</FONT>                data = new BigDecimal[nRows][nCols];<a name="line.732"></a>
<FONT color="green">733</FONT>                System.arraycopy(subMatrix, 0, data, 0, subMatrix.length);<a name="line.733"></a>
<FONT color="green">734</FONT>            } else {<a name="line.734"></a>
<FONT color="green">735</FONT>                MatrixUtils.checkRowIndex(this, row);<a name="line.735"></a>
<FONT color="green">736</FONT>                MatrixUtils.checkColumnIndex(this, column);<a name="line.736"></a>
<FONT color="green">737</FONT>                MatrixUtils.checkRowIndex(this, nRows + row - 1);<a name="line.737"></a>
<FONT color="green">738</FONT>                MatrixUtils.checkColumnIndex(this, nCols + column - 1);<a name="line.738"></a>
<FONT color="green">739</FONT>            }<a name="line.739"></a>
<FONT color="green">740</FONT>            for (int i = 0; i &lt; nRows; i++) {<a name="line.740"></a>
<FONT color="green">741</FONT>                System.arraycopy(subMatrix[i], 0, data[row + i], column, nCols);<a name="line.741"></a>
<FONT color="green">742</FONT>            }<a name="line.742"></a>
<FONT color="green">743</FONT>    <a name="line.743"></a>
<FONT color="green">744</FONT>            lu = null;<a name="line.744"></a>
<FONT color="green">745</FONT>    <a name="line.745"></a>
<FONT color="green">746</FONT>        }<a name="line.746"></a>
<FONT color="green">747</FONT>    <a name="line.747"></a>
<FONT color="green">748</FONT>        /**<a name="line.748"></a>
<FONT color="green">749</FONT>         * Returns the entries in row number &lt;code&gt;row&lt;/code&gt;<a name="line.749"></a>
<FONT color="green">750</FONT>         * as a row matrix.  Row indices start at 0.<a name="line.750"></a>
<FONT color="green">751</FONT>         *<a name="line.751"></a>
<FONT color="green">752</FONT>         * @param row the row to be fetched<a name="line.752"></a>
<FONT color="green">753</FONT>         * @return row matrix<a name="line.753"></a>
<FONT color="green">754</FONT>         * @throws MatrixIndexException if the specified row index is invalid<a name="line.754"></a>
<FONT color="green">755</FONT>         */<a name="line.755"></a>
<FONT color="green">756</FONT>        public BigMatrix getRowMatrix(int row) throws MatrixIndexException {<a name="line.756"></a>
<FONT color="green">757</FONT>            MatrixUtils.checkRowIndex(this, row);<a name="line.757"></a>
<FONT color="green">758</FONT>            final int ncols = this.getColumnDimension();<a name="line.758"></a>
<FONT color="green">759</FONT>            final BigDecimal[][] out = new BigDecimal[1][ncols];<a name="line.759"></a>
<FONT color="green">760</FONT>            System.arraycopy(data[row], 0, out[0], 0, ncols);<a name="line.760"></a>
<FONT color="green">761</FONT>            return new BigMatrixImpl(out, false);<a name="line.761"></a>
<FONT color="green">762</FONT>        }<a name="line.762"></a>
<FONT color="green">763</FONT>    <a name="line.763"></a>
<FONT color="green">764</FONT>        /**<a name="line.764"></a>
<FONT color="green">765</FONT>         * Returns the entries in column number &lt;code&gt;column&lt;/code&gt;<a name="line.765"></a>
<FONT color="green">766</FONT>         * as a column matrix.  Column indices start at 0.<a name="line.766"></a>
<FONT color="green">767</FONT>         *<a name="line.767"></a>
<FONT color="green">768</FONT>         * @param column the column to be fetched<a name="line.768"></a>
<FONT color="green">769</FONT>         * @return column matrix<a name="line.769"></a>
<FONT color="green">770</FONT>         * @throws MatrixIndexException if the specified column index is invalid<a name="line.770"></a>
<FONT color="green">771</FONT>         */<a name="line.771"></a>
<FONT color="green">772</FONT>        public BigMatrix getColumnMatrix(int column) throws MatrixIndexException {<a name="line.772"></a>
<FONT color="green">773</FONT>            MatrixUtils.checkColumnIndex(this, column);<a name="line.773"></a>
<FONT color="green">774</FONT>            final int nRows = this.getRowDimension();<a name="line.774"></a>
<FONT color="green">775</FONT>            final BigDecimal[][] out = new BigDecimal[nRows][1];<a name="line.775"></a>
<FONT color="green">776</FONT>            for (int row = 0; row &lt; nRows; row++) {<a name="line.776"></a>
<FONT color="green">777</FONT>                out[row][0] = data[row][column];<a name="line.777"></a>
<FONT color="green">778</FONT>            }<a name="line.778"></a>
<FONT color="green">779</FONT>            return new BigMatrixImpl(out, false);<a name="line.779"></a>
<FONT color="green">780</FONT>        }<a name="line.780"></a>
<FONT color="green">781</FONT>    <a name="line.781"></a>
<FONT color="green">782</FONT>        /**<a name="line.782"></a>
<FONT color="green">783</FONT>         * Returns the entries in row number &lt;code&gt;row&lt;/code&gt; as an array.<a name="line.783"></a>
<FONT color="green">784</FONT>         * &lt;p&gt;<a name="line.784"></a>
<FONT color="green">785</FONT>         * Row indices start at 0.  A &lt;code&gt;MatrixIndexException&lt;/code&gt; is thrown<a name="line.785"></a>
<FONT color="green">786</FONT>         * unless &lt;code&gt;0 &lt;= row &lt; rowDimension.&lt;/code&gt;&lt;/p&gt;<a name="line.786"></a>
<FONT color="green">787</FONT>         *<a name="line.787"></a>
<FONT color="green">788</FONT>         * @param row the row to be fetched<a name="line.788"></a>
<FONT color="green">789</FONT>         * @return array of entries in the row<a name="line.789"></a>
<FONT color="green">790</FONT>         * @throws MatrixIndexException if the specified row index is not valid<a name="line.790"></a>
<FONT color="green">791</FONT>         */<a name="line.791"></a>
<FONT color="green">792</FONT>        public BigDecimal[] getRow(int row) throws MatrixIndexException {<a name="line.792"></a>
<FONT color="green">793</FONT>            MatrixUtils.checkRowIndex(this, row);<a name="line.793"></a>
<FONT color="green">794</FONT>            final int ncols = this.getColumnDimension();<a name="line.794"></a>
<FONT color="green">795</FONT>            final BigDecimal[] out = new BigDecimal[ncols];<a name="line.795"></a>
<FONT color="green">796</FONT>            System.arraycopy(data[row], 0, out, 0, ncols);<a name="line.796"></a>
<FONT color="green">797</FONT>            return out;<a name="line.797"></a>
<FONT color="green">798</FONT>        }<a name="line.798"></a>
<FONT color="green">799</FONT>    <a name="line.799"></a>
<FONT color="green">800</FONT>         /**<a name="line.800"></a>
<FONT color="green">801</FONT>         * Returns the entries in row number &lt;code&gt;row&lt;/code&gt; as an array<a name="line.801"></a>
<FONT color="green">802</FONT>         * of double values.<a name="line.802"></a>
<FONT color="green">803</FONT>         * &lt;p&gt;<a name="line.803"></a>
<FONT color="green">804</FONT>         * Row indices start at 0.  A &lt;code&gt;MatrixIndexException&lt;/code&gt; is thrown<a name="line.804"></a>
<FONT color="green">805</FONT>         * unless &lt;code&gt;0 &lt;= row &lt; rowDimension.&lt;/code&gt;&lt;/p&gt;<a name="line.805"></a>
<FONT color="green">806</FONT>         *<a name="line.806"></a>
<FONT color="green">807</FONT>         * @param row the row to be fetched<a name="line.807"></a>
<FONT color="green">808</FONT>         * @return array of entries in the row<a name="line.808"></a>
<FONT color="green">809</FONT>         * @throws MatrixIndexException if the specified row index is not valid<a name="line.809"></a>
<FONT color="green">810</FONT>         */<a name="line.810"></a>
<FONT color="green">811</FONT>        public double[] getRowAsDoubleArray(int row) throws MatrixIndexException {<a name="line.811"></a>
<FONT color="green">812</FONT>            MatrixUtils.checkRowIndex(this, row);<a name="line.812"></a>
<FONT color="green">813</FONT>            final int ncols = this.getColumnDimension();<a name="line.813"></a>
<FONT color="green">814</FONT>            final double[] out = new double[ncols];<a name="line.814"></a>
<FONT color="green">815</FONT>            for (int i=0;i&lt;ncols;i++) {<a name="line.815"></a>
<FONT color="green">816</FONT>                out[i] = data[row][i].doubleValue();<a name="line.816"></a>
<FONT color="green">817</FONT>            }<a name="line.817"></a>
<FONT color="green">818</FONT>            return out;<a name="line.818"></a>
<FONT color="green">819</FONT>        }<a name="line.819"></a>
<FONT color="green">820</FONT>    <a name="line.820"></a>
<FONT color="green">821</FONT>         /**<a name="line.821"></a>
<FONT color="green">822</FONT>         * Returns the entries in column number &lt;code&gt;col&lt;/code&gt; as an array.<a name="line.822"></a>
<FONT color="green">823</FONT>         * &lt;p&gt;<a name="line.823"></a>
<FONT color="green">824</FONT>         * Column indices start at 0.  A &lt;code&gt;MatrixIndexException&lt;/code&gt; is thrown<a name="line.824"></a>
<FONT color="green">825</FONT>         * unless &lt;code&gt;0 &lt;= column &lt; columnDimension.&lt;/code&gt;&lt;/p&gt;<a name="line.825"></a>
<FONT color="green">826</FONT>         *<a name="line.826"></a>
<FONT color="green">827</FONT>         * @param col the column to be fetched<a name="line.827"></a>
<FONT color="green">828</FONT>         * @return array of entries in the column<a name="line.828"></a>
<FONT color="green">829</FONT>         * @throws MatrixIndexException if the specified column index is not valid<a name="line.829"></a>
<FONT color="green">830</FONT>         */<a name="line.830"></a>
<FONT color="green">831</FONT>        public BigDecimal[] getColumn(int col) throws MatrixIndexException {<a name="line.831"></a>
<FONT color="green">832</FONT>            MatrixUtils.checkColumnIndex(this, col);<a name="line.832"></a>
<FONT color="green">833</FONT>            final int nRows = this.getRowDimension();<a name="line.833"></a>
<FONT color="green">834</FONT>            final BigDecimal[] out = new BigDecimal[nRows];<a name="line.834"></a>
<FONT color="green">835</FONT>            for (int i = 0; i &lt; nRows; i++) {<a name="line.835"></a>
<FONT color="green">836</FONT>                out[i] = data[i][col];<a name="line.836"></a>
<FONT color="green">837</FONT>            }<a name="line.837"></a>
<FONT color="green">838</FONT>            return out;<a name="line.838"></a>
<FONT color="green">839</FONT>        }<a name="line.839"></a>
<FONT color="green">840</FONT>    <a name="line.840"></a>
<FONT color="green">841</FONT>        /**<a name="line.841"></a>
<FONT color="green">842</FONT>         * Returns the entries in column number &lt;code&gt;col&lt;/code&gt; as an array<a name="line.842"></a>
<FONT color="green">843</FONT>         * of double values.<a name="line.843"></a>
<FONT color="green">844</FONT>         * &lt;p&gt;<a name="line.844"></a>
<FONT color="green">845</FONT>         * Column indices start at 0.  A &lt;code&gt;MatrixIndexException&lt;/code&gt; is thrown<a name="line.845"></a>
<FONT color="green">846</FONT>         * unless &lt;code&gt;0 &lt;= column &lt; columnDimension.&lt;/code&gt;&lt;/p&gt;<a name="line.846"></a>
<FONT color="green">847</FONT>         *<a name="line.847"></a>
<FONT color="green">848</FONT>         * @param col the column to be fetched<a name="line.848"></a>
<FONT color="green">849</FONT>         * @return array of entries in the column<a name="line.849"></a>
<FONT color="green">850</FONT>         * @throws MatrixIndexException if the specified column index is not valid<a name="line.850"></a>
<FONT color="green">851</FONT>         */<a name="line.851"></a>
<FONT color="green">852</FONT>        public double[] getColumnAsDoubleArray(int col) throws MatrixIndexException {<a name="line.852"></a>
<FONT color="green">853</FONT>            MatrixUtils.checkColumnIndex(this, col);<a name="line.853"></a>
<FONT color="green">854</FONT>            final int nrows = this.getRowDimension();<a name="line.854"></a>
<FONT color="green">855</FONT>            final double[] out = new double[nrows];<a name="line.855"></a>
<FONT color="green">856</FONT>            for (int i=0;i&lt;nrows;i++) {<a name="line.856"></a>
<FONT color="green">857</FONT>                out[i] = data[i][col].doubleValue();<a name="line.857"></a>
<FONT color="green">858</FONT>            }<a name="line.858"></a>
<FONT color="green">859</FONT>            return out;<a name="line.859"></a>
<FONT color="green">860</FONT>        }<a name="line.860"></a>
<FONT color="green">861</FONT>    <a name="line.861"></a>
<FONT color="green">862</FONT>         /**<a name="line.862"></a>
<FONT color="green">863</FONT>         * Returns the entry in the specified row and column.<a name="line.863"></a>
<FONT color="green">864</FONT>         * &lt;p&gt;<a name="line.864"></a>
<FONT color="green">865</FONT>         * Row and column indices start at 0 and must satisfy<a name="line.865"></a>
<FONT color="green">866</FONT>         * &lt;ul&gt;<a name="line.866"></a>
<FONT color="green">867</FONT>         * &lt;li&gt;&lt;code&gt;0 &lt;= row &lt; rowDimension&lt;/code&gt;&lt;/li&gt;<a name="line.867"></a>
<FONT color="green">868</FONT>         * &lt;li&gt;&lt;code&gt; 0 &lt;= column &lt; columnDimension&lt;/code&gt;&lt;/li&gt;<a name="line.868"></a>
<FONT color="green">869</FONT>         * &lt;/ul&gt;<a name="line.869"></a>
<FONT color="green">870</FONT>         * otherwise a &lt;code&gt;MatrixIndexException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.870"></a>
<FONT color="green">871</FONT>         *<a name="line.871"></a>
<FONT color="green">872</FONT>         * @param row  row location of entry to be fetched<a name="line.872"></a>
<FONT color="green">873</FONT>         * @param column  column location of entry to be fetched<a name="line.873"></a>
<FONT color="green">874</FONT>         * @return matrix entry in row,column<a name="line.874"></a>
<FONT color="green">875</FONT>         * @throws MatrixIndexException if the row or column index is not valid<a name="line.875"></a>
<FONT color="green">876</FONT>         */<a name="line.876"></a>
<FONT color="green">877</FONT>        public BigDecimal getEntry(int row, int column)<a name="line.877"></a>
<FONT color="green">878</FONT>        throws MatrixIndexException {<a name="line.878"></a>
<FONT color="green">879</FONT>            try {<a name="line.879"></a>
<FONT color="green">880</FONT>                return data[row][column];<a name="line.880"></a>
<FONT color="green">881</FONT>            } catch (ArrayIndexOutOfBoundsException e) {<a name="line.881"></a>
<FONT color="green">882</FONT>                throw new MatrixIndexException(<a name="line.882"></a>
<FONT color="green">883</FONT>                        LocalizedFormats.NO_SUCH_MATRIX_ENTRY,<a name="line.883"></a>
<FONT color="green">884</FONT>                        row, column, getRowDimension(), getColumnDimension());<a name="line.884"></a>
<FONT color="green">885</FONT>            }<a name="line.885"></a>
<FONT color="green">886</FONT>        }<a name="line.886"></a>
<FONT color="green">887</FONT>    <a name="line.887"></a>
<FONT color="green">888</FONT>        /**<a name="line.888"></a>
<FONT color="green">889</FONT>         * Returns the entry in the specified row and column as a double.<a name="line.889"></a>
<FONT color="green">890</FONT>         * &lt;p&gt;<a name="line.890"></a>
<FONT color="green">891</FONT>         * Row and column indices start at 0 and must satisfy<a name="line.891"></a>
<FONT color="green">892</FONT>         * &lt;ul&gt;<a name="line.892"></a>
<FONT color="green">893</FONT>         * &lt;li&gt;&lt;code&gt;0 &lt;= row &lt; rowDimension&lt;/code&gt;&lt;/li&gt;<a name="line.893"></a>
<FONT color="green">894</FONT>         * &lt;li&gt;&lt;code&gt; 0 &lt;= column &lt; columnDimension&lt;/code&gt;&lt;/li&gt;<a name="line.894"></a>
<FONT color="green">895</FONT>         * &lt;/ul&gt;<a name="line.895"></a>
<FONT color="green">896</FONT>         * otherwise a &lt;code&gt;MatrixIndexException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.896"></a>
<FONT color="green">897</FONT>         *<a name="line.897"></a>
<FONT color="green">898</FONT>         * @param row  row location of entry to be fetched<a name="line.898"></a>
<FONT color="green">899</FONT>         * @param column  column location of entry to be fetched<a name="line.899"></a>
<FONT color="green">900</FONT>         * @return matrix entry in row,column<a name="line.900"></a>
<FONT color="green">901</FONT>         * @throws MatrixIndexException if the row<a name="line.901"></a>
<FONT color="green">902</FONT>         * or column index is not valid<a name="line.902"></a>
<FONT color="green">903</FONT>         */<a name="line.903"></a>
<FONT color="green">904</FONT>        public double getEntryAsDouble(int row, int column) throws MatrixIndexException {<a name="line.904"></a>
<FONT color="green">905</FONT>            return getEntry(row,column).doubleValue();<a name="line.905"></a>
<FONT color="green">906</FONT>        }<a name="line.906"></a>
<FONT color="green">907</FONT>    <a name="line.907"></a>
<FONT color="green">908</FONT>        /**<a name="line.908"></a>
<FONT color="green">909</FONT>         * Returns the transpose matrix.<a name="line.909"></a>
<FONT color="green">910</FONT>         *<a name="line.910"></a>
<FONT color="green">911</FONT>         * @return transpose matrix<a name="line.911"></a>
<FONT color="green">912</FONT>         */<a name="line.912"></a>
<FONT color="green">913</FONT>        public BigMatrix transpose() {<a name="line.913"></a>
<FONT color="green">914</FONT>            final int nRows = this.getRowDimension();<a name="line.914"></a>
<FONT color="green">915</FONT>            final int nCols = this.getColumnDimension();<a name="line.915"></a>
<FONT color="green">916</FONT>            final BigDecimal[][] outData = new BigDecimal[nCols][nRows];<a name="line.916"></a>
<FONT color="green">917</FONT>            for (int row = 0; row &lt; nRows; row++) {<a name="line.917"></a>
<FONT color="green">918</FONT>                final BigDecimal[] dataRow = data[row];<a name="line.918"></a>
<FONT color="green">919</FONT>                for (int col = 0; col &lt; nCols; col++) {<a name="line.919"></a>
<FONT color="green">920</FONT>                    outData[col][row] = dataRow[col];<a name="line.920"></a>
<FONT color="green">921</FONT>                }<a name="line.921"></a>
<FONT color="green">922</FONT>            }<a name="line.922"></a>
<FONT color="green">923</FONT>            return new BigMatrixImpl(outData, false);<a name="line.923"></a>
<FONT color="green">924</FONT>        }<a name="line.924"></a>
<FONT color="green">925</FONT>    <a name="line.925"></a>
<FONT color="green">926</FONT>        /**<a name="line.926"></a>
<FONT color="green">927</FONT>         * Returns the inverse matrix if this matrix is invertible.<a name="line.927"></a>
<FONT color="green">928</FONT>         *<a name="line.928"></a>
<FONT color="green">929</FONT>         * @return inverse matrix<a name="line.929"></a>
<FONT color="green">930</FONT>         * @throws InvalidMatrixException if this is not invertible<a name="line.930"></a>
<FONT color="green">931</FONT>         */<a name="line.931"></a>
<FONT color="green">932</FONT>        public BigMatrix inverse() throws InvalidMatrixException {<a name="line.932"></a>
<FONT color="green">933</FONT>            return solve(MatrixUtils.createBigIdentityMatrix(getRowDimension()));<a name="line.933"></a>
<FONT color="green">934</FONT>        }<a name="line.934"></a>
<FONT color="green">935</FONT>    <a name="line.935"></a>
<FONT color="green">936</FONT>        /**<a name="line.936"></a>
<FONT color="green">937</FONT>         * Returns the determinant of this matrix.<a name="line.937"></a>
<FONT color="green">938</FONT>         *<a name="line.938"></a>
<FONT color="green">939</FONT>         * @return determinant<a name="line.939"></a>
<FONT color="green">940</FONT>         * @throws InvalidMatrixException if matrix is not square<a name="line.940"></a>
<FONT color="green">941</FONT>         */<a name="line.941"></a>
<FONT color="green">942</FONT>        public BigDecimal getDeterminant() throws InvalidMatrixException {<a name="line.942"></a>
<FONT color="green">943</FONT>            if (!isSquare()) {<a name="line.943"></a>
<FONT color="green">944</FONT>                throw new NonSquareMatrixException(getRowDimension(), getColumnDimension());<a name="line.944"></a>
<FONT color="green">945</FONT>            }<a name="line.945"></a>
<FONT color="green">946</FONT>            if (isSingular()) {   // note: this has side effect of attempting LU decomp if lu == null<a name="line.946"></a>
<FONT color="green">947</FONT>                return ZERO;<a name="line.947"></a>
<FONT color="green">948</FONT>            } else {<a name="line.948"></a>
<FONT color="green">949</FONT>                BigDecimal det = (parity == 1) ? ONE : ONE.negate();<a name="line.949"></a>
<FONT color="green">950</FONT>                for (int i = 0; i &lt; getRowDimension(); i++) {<a name="line.950"></a>
<FONT color="green">951</FONT>                    det = det.multiply(lu[i][i]);<a name="line.951"></a>
<FONT color="green">952</FONT>                }<a name="line.952"></a>
<FONT color="green">953</FONT>                return det;<a name="line.953"></a>
<FONT color="green">954</FONT>            }<a name="line.954"></a>
<FONT color="green">955</FONT>        }<a name="line.955"></a>
<FONT color="green">956</FONT>    <a name="line.956"></a>
<FONT color="green">957</FONT>         /**<a name="line.957"></a>
<FONT color="green">958</FONT>         * Is this a square matrix?<a name="line.958"></a>
<FONT color="green">959</FONT>         * @return true if the matrix is square (rowDimension = columnDimension)<a name="line.959"></a>
<FONT color="green">960</FONT>         */<a name="line.960"></a>
<FONT color="green">961</FONT>        public boolean isSquare() {<a name="line.961"></a>
<FONT color="green">962</FONT>            return getColumnDimension() == getRowDimension();<a name="line.962"></a>
<FONT color="green">963</FONT>        }<a name="line.963"></a>
<FONT color="green">964</FONT>    <a name="line.964"></a>
<FONT color="green">965</FONT>        /**<a name="line.965"></a>
<FONT color="green">966</FONT>         * Is this a singular matrix?<a name="line.966"></a>
<FONT color="green">967</FONT>         * @return true if the matrix is singular<a name="line.967"></a>
<FONT color="green">968</FONT>         */<a name="line.968"></a>
<FONT color="green">969</FONT>        public boolean isSingular() {<a name="line.969"></a>
<FONT color="green">970</FONT>            if (lu == null) {<a name="line.970"></a>
<FONT color="green">971</FONT>                try {<a name="line.971"></a>
<FONT color="green">972</FONT>                    luDecompose();<a name="line.972"></a>
<FONT color="green">973</FONT>                    return false;<a name="line.973"></a>
<FONT color="green">974</FONT>                } catch (InvalidMatrixException ex) {<a name="line.974"></a>
<FONT color="green">975</FONT>                    return true;<a name="line.975"></a>
<FONT color="green">976</FONT>                }<a name="line.976"></a>
<FONT color="green">977</FONT>            } else { // LU decomp must have been successfully performed<a name="line.977"></a>
<FONT color="green">978</FONT>                return false; // so the matrix is not singular<a name="line.978"></a>
<FONT color="green">979</FONT>            }<a name="line.979"></a>
<FONT color="green">980</FONT>        }<a name="line.980"></a>
<FONT color="green">981</FONT>    <a name="line.981"></a>
<FONT color="green">982</FONT>        /**<a name="line.982"></a>
<FONT color="green">983</FONT>         * Returns the number of rows in the matrix.<a name="line.983"></a>
<FONT color="green">984</FONT>         *<a name="line.984"></a>
<FONT color="green">985</FONT>         * @return rowDimension<a name="line.985"></a>
<FONT color="green">986</FONT>         */<a name="line.986"></a>
<FONT color="green">987</FONT>        public int getRowDimension() {<a name="line.987"></a>
<FONT color="green">988</FONT>            return data.length;<a name="line.988"></a>
<FONT color="green">989</FONT>        }<a name="line.989"></a>
<FONT color="green">990</FONT>    <a name="line.990"></a>
<FONT color="green">991</FONT>        /**<a name="line.991"></a>
<FONT color="green">992</FONT>         * Returns the number of columns in the matrix.<a name="line.992"></a>
<FONT color="green">993</FONT>         *<a name="line.993"></a>
<FONT color="green">994</FONT>         * @return columnDimension<a name="line.994"></a>
<FONT color="green">995</FONT>         */<a name="line.995"></a>
<FONT color="green">996</FONT>        public int getColumnDimension() {<a name="line.996"></a>
<FONT color="green">997</FONT>            return data[0].length;<a name="line.997"></a>
<FONT color="green">998</FONT>        }<a name="line.998"></a>
<FONT color="green">999</FONT>    <a name="line.999"></a>
<FONT color="green">1000</FONT>         /**<a name="line.1000"></a>
<FONT color="green">1001</FONT>         * Returns the &lt;a href="http://mathworld.wolfram.com/MatrixTrace.html"&gt;<a name="line.1001"></a>
<FONT color="green">1002</FONT>         * trace&lt;/a&gt; of the matrix (the sum of the elements on the main diagonal).<a name="line.1002"></a>
<FONT color="green">1003</FONT>         *<a name="line.1003"></a>
<FONT color="green">1004</FONT>         * @return trace<a name="line.1004"></a>
<FONT color="green">1005</FONT>         *<a name="line.1005"></a>
<FONT color="green">1006</FONT>         * @throws IllegalArgumentException if this matrix is not square.<a name="line.1006"></a>
<FONT color="green">1007</FONT>         */<a name="line.1007"></a>
<FONT color="green">1008</FONT>        public BigDecimal getTrace() throws IllegalArgumentException {<a name="line.1008"></a>
<FONT color="green">1009</FONT>            if (!isSquare()) {<a name="line.1009"></a>
<FONT color="green">1010</FONT>                throw new NonSquareMatrixException(getRowDimension(), getColumnDimension());<a name="line.1010"></a>
<FONT color="green">1011</FONT>            }<a name="line.1011"></a>
<FONT color="green">1012</FONT>            BigDecimal trace = data[0][0];<a name="line.1012"></a>
<FONT color="green">1013</FONT>            for (int i = 1; i &lt; this.getRowDimension(); i++) {<a name="line.1013"></a>
<FONT color="green">1014</FONT>                trace = trace.add(data[i][i]);<a name="line.1014"></a>
<FONT color="green">1015</FONT>            }<a name="line.1015"></a>
<FONT color="green">1016</FONT>            return trace;<a name="line.1016"></a>
<FONT color="green">1017</FONT>        }<a name="line.1017"></a>
<FONT color="green">1018</FONT>    <a name="line.1018"></a>
<FONT color="green">1019</FONT>        /**<a name="line.1019"></a>
<FONT color="green">1020</FONT>         * Returns the result of multiplying this by the vector &lt;code&gt;v&lt;/code&gt;.<a name="line.1020"></a>
<FONT color="green">1021</FONT>         *<a name="line.1021"></a>
<FONT color="green">1022</FONT>         * @param v the vector to operate on<a name="line.1022"></a>
<FONT color="green">1023</FONT>         * @return this*v<a name="line.1023"></a>
<FONT color="green">1024</FONT>         * @throws IllegalArgumentException if columnDimension != v.size()<a name="line.1024"></a>
<FONT color="green">1025</FONT>         */<a name="line.1025"></a>
<FONT color="green">1026</FONT>        public BigDecimal[] operate(BigDecimal[] v) throws IllegalArgumentException {<a name="line.1026"></a>
<FONT color="green">1027</FONT>            if (v.length != getColumnDimension()) {<a name="line.1027"></a>
<FONT color="green">1028</FONT>                throw MathRuntimeException.createIllegalArgumentException(<a name="line.1028"></a>
<FONT color="green">1029</FONT>                        LocalizedFormats.VECTOR_LENGTH_MISMATCH,<a name="line.1029"></a>
<FONT color="green">1030</FONT>                        v.length, getColumnDimension() );<a name="line.1030"></a>
<FONT color="green">1031</FONT>            }<a name="line.1031"></a>
<FONT color="green">1032</FONT>            final int nRows = this.getRowDimension();<a name="line.1032"></a>
<FONT color="green">1033</FONT>            final int nCols = this.getColumnDimension();<a name="line.1033"></a>
<FONT color="green">1034</FONT>            final BigDecimal[] out = new BigDecimal[nRows];<a name="line.1034"></a>
<FONT color="green">1035</FONT>            for (int row = 0; row &lt; nRows; row++) {<a name="line.1035"></a>
<FONT color="green">1036</FONT>                BigDecimal sum = ZERO;<a name="line.1036"></a>
<FONT color="green">1037</FONT>                for (int i = 0; i &lt; nCols; i++) {<a name="line.1037"></a>
<FONT color="green">1038</FONT>                    sum = sum.add(data[row][i].multiply(v[i]));<a name="line.1038"></a>
<FONT color="green">1039</FONT>                }<a name="line.1039"></a>
<FONT color="green">1040</FONT>                out[row] = sum;<a name="line.1040"></a>
<FONT color="green">1041</FONT>            }<a name="line.1041"></a>
<FONT color="green">1042</FONT>            return out;<a name="line.1042"></a>
<FONT color="green">1043</FONT>        }<a name="line.1043"></a>
<FONT color="green">1044</FONT>    <a name="line.1044"></a>
<FONT color="green">1045</FONT>        /**<a name="line.1045"></a>
<FONT color="green">1046</FONT>         * Returns the result of multiplying this by the vector &lt;code&gt;v&lt;/code&gt;.<a name="line.1046"></a>
<FONT color="green">1047</FONT>         *<a name="line.1047"></a>
<FONT color="green">1048</FONT>         * @param v the vector to operate on<a name="line.1048"></a>
<FONT color="green">1049</FONT>         * @return this*v<a name="line.1049"></a>
<FONT color="green">1050</FONT>         * @throws IllegalArgumentException if columnDimension != v.size()<a name="line.1050"></a>
<FONT color="green">1051</FONT>         */<a name="line.1051"></a>
<FONT color="green">1052</FONT>        public BigDecimal[] operate(double[] v) throws IllegalArgumentException {<a name="line.1052"></a>
<FONT color="green">1053</FONT>            final BigDecimal bd[] = new BigDecimal[v.length];<a name="line.1053"></a>
<FONT color="green">1054</FONT>            for (int i = 0; i &lt; bd.length; i++) {<a name="line.1054"></a>
<FONT color="green">1055</FONT>                bd[i] = new BigDecimal(v[i]);<a name="line.1055"></a>
<FONT color="green">1056</FONT>            }<a name="line.1056"></a>
<FONT color="green">1057</FONT>            return operate(bd);<a name="line.1057"></a>
<FONT color="green">1058</FONT>        }<a name="line.1058"></a>
<FONT color="green">1059</FONT>    <a name="line.1059"></a>
<FONT color="green">1060</FONT>        /**<a name="line.1060"></a>
<FONT color="green">1061</FONT>         * Returns the (row) vector result of premultiplying this by the vector &lt;code&gt;v&lt;/code&gt;.<a name="line.1061"></a>
<FONT color="green">1062</FONT>         *<a name="line.1062"></a>
<FONT color="green">1063</FONT>         * @param v the row vector to premultiply by<a name="line.1063"></a>
<FONT color="green">1064</FONT>         * @return v*this<a name="line.1064"></a>
<FONT color="green">1065</FONT>         * @throws IllegalArgumentException if rowDimension != v.size()<a name="line.1065"></a>
<FONT color="green">1066</FONT>         */<a name="line.1066"></a>
<FONT color="green">1067</FONT>        public BigDecimal[] preMultiply(BigDecimal[] v) throws IllegalArgumentException {<a name="line.1067"></a>
<FONT color="green">1068</FONT>            final int nRows = this.getRowDimension();<a name="line.1068"></a>
<FONT color="green">1069</FONT>            if (v.length != nRows) {<a name="line.1069"></a>
<FONT color="green">1070</FONT>                throw MathRuntimeException.createIllegalArgumentException(<a name="line.1070"></a>
<FONT color="green">1071</FONT>                        LocalizedFormats.VECTOR_LENGTH_MISMATCH,<a name="line.1071"></a>
<FONT color="green">1072</FONT>                        v.length, nRows );<a name="line.1072"></a>
<FONT color="green">1073</FONT>            }<a name="line.1073"></a>
<FONT color="green">1074</FONT>            final int nCols = this.getColumnDimension();<a name="line.1074"></a>
<FONT color="green">1075</FONT>            final BigDecimal[] out = new BigDecimal[nCols];<a name="line.1075"></a>
<FONT color="green">1076</FONT>            for (int col = 0; col &lt; nCols; col++) {<a name="line.1076"></a>
<FONT color="green">1077</FONT>                BigDecimal sum = ZERO;<a name="line.1077"></a>
<FONT color="green">1078</FONT>                for (int i = 0; i &lt; nRows; i++) {<a name="line.1078"></a>
<FONT color="green">1079</FONT>                    sum = sum.add(data[i][col].multiply(v[i]));<a name="line.1079"></a>
<FONT color="green">1080</FONT>                }<a name="line.1080"></a>
<FONT color="green">1081</FONT>                out[col] = sum;<a name="line.1081"></a>
<FONT color="green">1082</FONT>            }<a name="line.1082"></a>
<FONT color="green">1083</FONT>            return out;<a name="line.1083"></a>
<FONT color="green">1084</FONT>        }<a name="line.1084"></a>
<FONT color="green">1085</FONT>    <a name="line.1085"></a>
<FONT color="green">1086</FONT>        /**<a name="line.1086"></a>
<FONT color="green">1087</FONT>         * Returns a matrix of (column) solution vectors for linear systems with<a name="line.1087"></a>
<FONT color="green">1088</FONT>         * coefficient matrix = this and constant vectors = columns of<a name="line.1088"></a>
<FONT color="green">1089</FONT>         * &lt;code&gt;b&lt;/code&gt;.<a name="line.1089"></a>
<FONT color="green">1090</FONT>         *<a name="line.1090"></a>
<FONT color="green">1091</FONT>         * @param b  array of constants forming RHS of linear systems to<a name="line.1091"></a>
<FONT color="green">1092</FONT>         * to solve<a name="line.1092"></a>
<FONT color="green">1093</FONT>         * @return solution array<a name="line.1093"></a>
<FONT color="green">1094</FONT>         * @throws IllegalArgumentException if this.rowDimension != row dimension<a name="line.1094"></a>
<FONT color="green">1095</FONT>         * @throws InvalidMatrixException if this matrix is not square or is singular<a name="line.1095"></a>
<FONT color="green">1096</FONT>         */<a name="line.1096"></a>
<FONT color="green">1097</FONT>        public BigDecimal[] solve(BigDecimal[] b) throws IllegalArgumentException, InvalidMatrixException {<a name="line.1097"></a>
<FONT color="green">1098</FONT>            final int nRows = this.getRowDimension();<a name="line.1098"></a>
<FONT color="green">1099</FONT>            if (b.length != nRows) {<a name="line.1099"></a>
<FONT color="green">1100</FONT>                throw MathRuntimeException.createIllegalArgumentException(<a name="line.1100"></a>
<FONT color="green">1101</FONT>                        LocalizedFormats.VECTOR_LENGTH_MISMATCH,<a name="line.1101"></a>
<FONT color="green">1102</FONT>                        b.length, nRows);<a name="line.1102"></a>
<FONT color="green">1103</FONT>            }<a name="line.1103"></a>
<FONT color="green">1104</FONT>            final BigMatrix bMatrix = new BigMatrixImpl(b);<a name="line.1104"></a>
<FONT color="green">1105</FONT>            final BigDecimal[][] solution = ((BigMatrixImpl) (solve(bMatrix))).getDataRef();<a name="line.1105"></a>
<FONT color="green">1106</FONT>            final BigDecimal[] out = new BigDecimal[nRows];<a name="line.1106"></a>
<FONT color="green">1107</FONT>            for (int row = 0; row &lt; nRows; row++) {<a name="line.1107"></a>
<FONT color="green">1108</FONT>                out[row] = solution[row][0];<a name="line.1108"></a>
<FONT color="green">1109</FONT>            }<a name="line.1109"></a>
<FONT color="green">1110</FONT>            return out;<a name="line.1110"></a>
<FONT color="green">1111</FONT>        }<a name="line.1111"></a>
<FONT color="green">1112</FONT>    <a name="line.1112"></a>
<FONT color="green">1113</FONT>        /**<a name="line.1113"></a>
<FONT color="green">1114</FONT>         * Returns a matrix of (column) solution vectors for linear systems with<a name="line.1114"></a>
<FONT color="green">1115</FONT>         * coefficient matrix = this and constant vectors = columns of<a name="line.1115"></a>
<FONT color="green">1116</FONT>         * &lt;code&gt;b&lt;/code&gt;.<a name="line.1116"></a>
<FONT color="green">1117</FONT>         *<a name="line.1117"></a>
<FONT color="green">1118</FONT>         * @param b  array of constants forming RHS of linear systems to<a name="line.1118"></a>
<FONT color="green">1119</FONT>         * to solve<a name="line.1119"></a>
<FONT color="green">1120</FONT>         * @return solution array<a name="line.1120"></a>
<FONT color="green">1121</FONT>         * @throws IllegalArgumentException if this.rowDimension != row dimension<a name="line.1121"></a>
<FONT color="green">1122</FONT>         * @throws InvalidMatrixException if this matrix is not square or is singular<a name="line.1122"></a>
<FONT color="green">1123</FONT>         */<a name="line.1123"></a>
<FONT color="green">1124</FONT>        public BigDecimal[] solve(double[] b) throws IllegalArgumentException, InvalidMatrixException {<a name="line.1124"></a>
<FONT color="green">1125</FONT>            final BigDecimal bd[] = new BigDecimal[b.length];<a name="line.1125"></a>
<FONT color="green">1126</FONT>            for (int i = 0; i &lt; bd.length; i++) {<a name="line.1126"></a>
<FONT color="green">1127</FONT>                bd[i] = new BigDecimal(b[i]);<a name="line.1127"></a>
<FONT color="green">1128</FONT>            }<a name="line.1128"></a>
<FONT color="green">1129</FONT>            return solve(bd);<a name="line.1129"></a>
<FONT color="green">1130</FONT>        }<a name="line.1130"></a>
<FONT color="green">1131</FONT>    <a name="line.1131"></a>
<FONT color="green">1132</FONT>        /**<a name="line.1132"></a>
<FONT color="green">1133</FONT>         * Returns a matrix of (column) solution vectors for linear systems with<a name="line.1133"></a>
<FONT color="green">1134</FONT>         * coefficient matrix = this and constant vectors = columns of<a name="line.1134"></a>
<FONT color="green">1135</FONT>         * &lt;code&gt;b&lt;/code&gt;.<a name="line.1135"></a>
<FONT color="green">1136</FONT>         *<a name="line.1136"></a>
<FONT color="green">1137</FONT>         * @param b  matrix of constant vectors forming RHS of linear systems to<a name="line.1137"></a>
<FONT color="green">1138</FONT>         * to solve<a name="line.1138"></a>
<FONT color="green">1139</FONT>         * @return matrix of solution vectors<a name="line.1139"></a>
<FONT color="green">1140</FONT>         * @throws IllegalArgumentException if this.rowDimension != row dimension<a name="line.1140"></a>
<FONT color="green">1141</FONT>         * @throws InvalidMatrixException if this matrix is not square or is singular<a name="line.1141"></a>
<FONT color="green">1142</FONT>         */<a name="line.1142"></a>
<FONT color="green">1143</FONT>        public BigMatrix solve(BigMatrix b) throws IllegalArgumentException, InvalidMatrixException  {<a name="line.1143"></a>
<FONT color="green">1144</FONT>            if (b.getRowDimension() != getRowDimension()) {<a name="line.1144"></a>
<FONT color="green">1145</FONT>                throw MathRuntimeException.createIllegalArgumentException(<a name="line.1145"></a>
<FONT color="green">1146</FONT>                        LocalizedFormats.DIMENSIONS_MISMATCH_2x2,<a name="line.1146"></a>
<FONT color="green">1147</FONT>                        b.getRowDimension(), b.getColumnDimension(), getRowDimension(), "n");<a name="line.1147"></a>
<FONT color="green">1148</FONT>            }<a name="line.1148"></a>
<FONT color="green">1149</FONT>            if (!isSquare()) {<a name="line.1149"></a>
<FONT color="green">1150</FONT>                throw new NonSquareMatrixException(getRowDimension(), getColumnDimension());<a name="line.1150"></a>
<FONT color="green">1151</FONT>            }<a name="line.1151"></a>
<FONT color="green">1152</FONT>            if (this.isSingular()) { // side effect: compute LU decomp<a name="line.1152"></a>
<FONT color="green">1153</FONT>                throw new SingularMatrixException();<a name="line.1153"></a>
<FONT color="green">1154</FONT>            }<a name="line.1154"></a>
<FONT color="green">1155</FONT>    <a name="line.1155"></a>
<FONT color="green">1156</FONT>            final int nCol = this.getColumnDimension();<a name="line.1156"></a>
<FONT color="green">1157</FONT>            final int nColB = b.getColumnDimension();<a name="line.1157"></a>
<FONT color="green">1158</FONT>            final int nRowB = b.getRowDimension();<a name="line.1158"></a>
<FONT color="green">1159</FONT>    <a name="line.1159"></a>
<FONT color="green">1160</FONT>            // Apply permutations to b<a name="line.1160"></a>
<FONT color="green">1161</FONT>            final BigDecimal[][] bp = new BigDecimal[nRowB][nColB];<a name="line.1161"></a>
<FONT color="green">1162</FONT>            for (int row = 0; row &lt; nRowB; row++) {<a name="line.1162"></a>
<FONT color="green">1163</FONT>                final BigDecimal[] bpRow = bp[row];<a name="line.1163"></a>
<FONT color="green">1164</FONT>                for (int col = 0; col &lt; nColB; col++) {<a name="line.1164"></a>
<FONT color="green">1165</FONT>                    bpRow[col] = b.getEntry(permutation[row], col);<a name="line.1165"></a>
<FONT color="green">1166</FONT>                }<a name="line.1166"></a>
<FONT color="green">1167</FONT>            }<a name="line.1167"></a>
<FONT color="green">1168</FONT>    <a name="line.1168"></a>
<FONT color="green">1169</FONT>            // Solve LY = b<a name="line.1169"></a>
<FONT color="green">1170</FONT>            for (int col = 0; col &lt; nCol; col++) {<a name="line.1170"></a>
<FONT color="green">1171</FONT>                for (int i = col + 1; i &lt; nCol; i++) {<a name="line.1171"></a>
<FONT color="green">1172</FONT>                    final BigDecimal[] bpI = bp[i];<a name="line.1172"></a>
<FONT color="green">1173</FONT>                    final BigDecimal[] luI = lu[i];<a name="line.1173"></a>
<FONT color="green">1174</FONT>                    for (int j = 0; j &lt; nColB; j++) {<a name="line.1174"></a>
<FONT color="green">1175</FONT>                        bpI[j] = bpI[j].subtract(bp[col][j].multiply(luI[col]));<a name="line.1175"></a>
<FONT color="green">1176</FONT>                    }<a name="line.1176"></a>
<FONT color="green">1177</FONT>                }<a name="line.1177"></a>
<FONT color="green">1178</FONT>            }<a name="line.1178"></a>
<FONT color="green">1179</FONT>    <a name="line.1179"></a>
<FONT color="green">1180</FONT>            // Solve UX = Y<a name="line.1180"></a>
<FONT color="green">1181</FONT>            for (int col = nCol - 1; col &gt;= 0; col--) {<a name="line.1181"></a>
<FONT color="green">1182</FONT>                final BigDecimal[] bpCol = bp[col];<a name="line.1182"></a>
<FONT color="green">1183</FONT>                final BigDecimal luDiag = lu[col][col];<a name="line.1183"></a>
<FONT color="green">1184</FONT>                for (int j = 0; j &lt; nColB; j++) {<a name="line.1184"></a>
<FONT color="green">1185</FONT>                    bpCol[j] = bpCol[j].divide(luDiag, scale, roundingMode);<a name="line.1185"></a>
<FONT color="green">1186</FONT>                }<a name="line.1186"></a>
<FONT color="green">1187</FONT>                for (int i = 0; i &lt; col; i++) {<a name="line.1187"></a>
<FONT color="green">1188</FONT>                    final BigDecimal[] bpI = bp[i];<a name="line.1188"></a>
<FONT color="green">1189</FONT>                    final BigDecimal[] luI = lu[i];<a name="line.1189"></a>
<FONT color="green">1190</FONT>                    for (int j = 0; j &lt; nColB; j++) {<a name="line.1190"></a>
<FONT color="green">1191</FONT>                        bpI[j] = bpI[j].subtract(bp[col][j].multiply(luI[col]));<a name="line.1191"></a>
<FONT color="green">1192</FONT>                    }<a name="line.1192"></a>
<FONT color="green">1193</FONT>                }<a name="line.1193"></a>
<FONT color="green">1194</FONT>            }<a name="line.1194"></a>
<FONT color="green">1195</FONT>    <a name="line.1195"></a>
<FONT color="green">1196</FONT>            return new BigMatrixImpl(bp, false);<a name="line.1196"></a>
<FONT color="green">1197</FONT>    <a name="line.1197"></a>
<FONT color="green">1198</FONT>        }<a name="line.1198"></a>
<FONT color="green">1199</FONT>    <a name="line.1199"></a>
<FONT color="green">1200</FONT>        /**<a name="line.1200"></a>
<FONT color="green">1201</FONT>         * Computes a new<a name="line.1201"></a>
<FONT color="green">1202</FONT>         * &lt;a href="http://www.math.gatech.edu/~bourbaki/math2601/Web-notes/2num.pdf"&gt;<a name="line.1202"></a>
<FONT color="green">1203</FONT>         * LU decompostion&lt;/a&gt; for this matrix, storing the result for use by other methods.<a name="line.1203"></a>
<FONT color="green">1204</FONT>         * &lt;p&gt;<a name="line.1204"></a>
<FONT color="green">1205</FONT>         * &lt;strong&gt;Implementation Note&lt;/strong&gt;:&lt;br&gt;<a name="line.1205"></a>
<FONT color="green">1206</FONT>         * Uses &lt;a href="http://www.damtp.cam.ac.uk/user/fdl/people/sd/lectures/nummeth98/linear.htm"&gt;<a name="line.1206"></a>
<FONT color="green">1207</FONT>         * Crout's algortithm&lt;/a&gt;, with partial pivoting.&lt;/p&gt;<a name="line.1207"></a>
<FONT color="green">1208</FONT>         * &lt;p&gt;<a name="line.1208"></a>
<FONT color="green">1209</FONT>         * &lt;strong&gt;Usage Note&lt;/strong&gt;:&lt;br&gt;<a name="line.1209"></a>
<FONT color="green">1210</FONT>         * This method should rarely be invoked directly. Its only use is<a name="line.1210"></a>
<FONT color="green">1211</FONT>         * to force recomputation of the LU decomposition when changes have been<a name="line.1211"></a>
<FONT color="green">1212</FONT>         * made to the underlying data using direct array references. Changes<a name="line.1212"></a>
<FONT color="green">1213</FONT>         * made using setXxx methods will trigger recomputation when needed<a name="line.1213"></a>
<FONT color="green">1214</FONT>         * automatically.&lt;/p&gt;<a name="line.1214"></a>
<FONT color="green">1215</FONT>         *<a name="line.1215"></a>
<FONT color="green">1216</FONT>         * @throws InvalidMatrixException if the matrix is non-square or singular.<a name="line.1216"></a>
<FONT color="green">1217</FONT>         */<a name="line.1217"></a>
<FONT color="green">1218</FONT>        public void luDecompose() throws InvalidMatrixException {<a name="line.1218"></a>
<FONT color="green">1219</FONT>    <a name="line.1219"></a>
<FONT color="green">1220</FONT>            final int nRows = this.getRowDimension();<a name="line.1220"></a>
<FONT color="green">1221</FONT>            final int nCols = this.getColumnDimension();<a name="line.1221"></a>
<FONT color="green">1222</FONT>            if (nRows != nCols) {<a name="line.1222"></a>
<FONT color="green">1223</FONT>                throw new NonSquareMatrixException(getRowDimension(), getColumnDimension());<a name="line.1223"></a>
<FONT color="green">1224</FONT>            }<a name="line.1224"></a>
<FONT color="green">1225</FONT>            lu = this.getData();<a name="line.1225"></a>
<FONT color="green">1226</FONT>    <a name="line.1226"></a>
<FONT color="green">1227</FONT>            // Initialize permutation array and parity<a name="line.1227"></a>
<FONT color="green">1228</FONT>            permutation = new int[nRows];<a name="line.1228"></a>
<FONT color="green">1229</FONT>            for (int row = 0; row &lt; nRows; row++) {<a name="line.1229"></a>
<FONT color="green">1230</FONT>                permutation[row] = row;<a name="line.1230"></a>
<FONT color="green">1231</FONT>            }<a name="line.1231"></a>
<FONT color="green">1232</FONT>            parity = 1;<a name="line.1232"></a>
<FONT color="green">1233</FONT>    <a name="line.1233"></a>
<FONT color="green">1234</FONT>            // Loop over columns<a name="line.1234"></a>
<FONT color="green">1235</FONT>            for (int col = 0; col &lt; nCols; col++) {<a name="line.1235"></a>
<FONT color="green">1236</FONT>    <a name="line.1236"></a>
<FONT color="green">1237</FONT>                BigDecimal sum = ZERO;<a name="line.1237"></a>
<FONT color="green">1238</FONT>    <a name="line.1238"></a>
<FONT color="green">1239</FONT>                // upper<a name="line.1239"></a>
<FONT color="green">1240</FONT>                for (int row = 0; row &lt; col; row++) {<a name="line.1240"></a>
<FONT color="green">1241</FONT>                    final BigDecimal[] luRow = lu[row];<a name="line.1241"></a>
<FONT color="green">1242</FONT>                    sum = luRow[col];<a name="line.1242"></a>
<FONT color="green">1243</FONT>                    for (int i = 0; i &lt; row; i++) {<a name="line.1243"></a>
<FONT color="green">1244</FONT>                        sum = sum.subtract(luRow[i].multiply(lu[i][col]));<a name="line.1244"></a>
<FONT color="green">1245</FONT>                    }<a name="line.1245"></a>
<FONT color="green">1246</FONT>                    luRow[col] = sum;<a name="line.1246"></a>
<FONT color="green">1247</FONT>                }<a name="line.1247"></a>
<FONT color="green">1248</FONT>    <a name="line.1248"></a>
<FONT color="green">1249</FONT>                // lower<a name="line.1249"></a>
<FONT color="green">1250</FONT>                int max = col; // permutation row<a name="line.1250"></a>
<FONT color="green">1251</FONT>                BigDecimal largest = ZERO;<a name="line.1251"></a>
<FONT color="green">1252</FONT>                for (int row = col; row &lt; nRows; row++) {<a name="line.1252"></a>
<FONT color="green">1253</FONT>                    final BigDecimal[] luRow = lu[row];<a name="line.1253"></a>
<FONT color="green">1254</FONT>                    sum = luRow[col];<a name="line.1254"></a>
<FONT color="green">1255</FONT>                    for (int i = 0; i &lt; col; i++) {<a name="line.1255"></a>
<FONT color="green">1256</FONT>                        sum = sum.subtract(luRow[i].multiply(lu[i][col]));<a name="line.1256"></a>
<FONT color="green">1257</FONT>                    }<a name="line.1257"></a>
<FONT color="green">1258</FONT>                    luRow[col] = sum;<a name="line.1258"></a>
<FONT color="green">1259</FONT>    <a name="line.1259"></a>
<FONT color="green">1260</FONT>                    // maintain best permutation choice<a name="line.1260"></a>
<FONT color="green">1261</FONT>                    if (sum.abs().compareTo(largest) == 1) {<a name="line.1261"></a>
<FONT color="green">1262</FONT>                        largest = sum.abs();<a name="line.1262"></a>
<FONT color="green">1263</FONT>                        max = row;<a name="line.1263"></a>
<FONT color="green">1264</FONT>                    }<a name="line.1264"></a>
<FONT color="green">1265</FONT>                }<a name="line.1265"></a>
<FONT color="green">1266</FONT>    <a name="line.1266"></a>
<FONT color="green">1267</FONT>                // Singularity check<a name="line.1267"></a>
<FONT color="green">1268</FONT>                if (lu[max][col].abs().compareTo(TOO_SMALL) &lt;= 0) {<a name="line.1268"></a>
<FONT color="green">1269</FONT>                    lu = null;<a name="line.1269"></a>
<FONT color="green">1270</FONT>                    throw new SingularMatrixException();<a name="line.1270"></a>
<FONT color="green">1271</FONT>                }<a name="line.1271"></a>
<FONT color="green">1272</FONT>    <a name="line.1272"></a>
<FONT color="green">1273</FONT>                // Pivot if necessary<a name="line.1273"></a>
<FONT color="green">1274</FONT>                if (max != col) {<a name="line.1274"></a>
<FONT color="green">1275</FONT>                    BigDecimal tmp = ZERO;<a name="line.1275"></a>
<FONT color="green">1276</FONT>                    for (int i = 0; i &lt; nCols; i++) {<a name="line.1276"></a>
<FONT color="green">1277</FONT>                        tmp = lu[max][i];<a name="line.1277"></a>
<FONT color="green">1278</FONT>                        lu[max][i] = lu[col][i];<a name="line.1278"></a>
<FONT color="green">1279</FONT>                        lu[col][i] = tmp;<a name="line.1279"></a>
<FONT color="green">1280</FONT>                    }<a name="line.1280"></a>
<FONT color="green">1281</FONT>                    int temp = permutation[max];<a name="line.1281"></a>
<FONT color="green">1282</FONT>                    permutation[max] = permutation[col];<a name="line.1282"></a>
<FONT color="green">1283</FONT>                    permutation[col] = temp;<a name="line.1283"></a>
<FONT color="green">1284</FONT>                    parity = -parity;<a name="line.1284"></a>
<FONT color="green">1285</FONT>                }<a name="line.1285"></a>
<FONT color="green">1286</FONT>    <a name="line.1286"></a>
<FONT color="green">1287</FONT>                // Divide the lower elements by the "winning" diagonal elt.<a name="line.1287"></a>
<FONT color="green">1288</FONT>                final BigDecimal luDiag = lu[col][col];<a name="line.1288"></a>
<FONT color="green">1289</FONT>                for (int row = col + 1; row &lt; nRows; row++) {<a name="line.1289"></a>
<FONT color="green">1290</FONT>                    final BigDecimal[] luRow = lu[row];<a name="line.1290"></a>
<FONT color="green">1291</FONT>                    luRow[col] = luRow[col].divide(luDiag, scale, roundingMode);<a name="line.1291"></a>
<FONT color="green">1292</FONT>                }<a name="line.1292"></a>
<FONT color="green">1293</FONT>    <a name="line.1293"></a>
<FONT color="green">1294</FONT>            }<a name="line.1294"></a>
<FONT color="green">1295</FONT>    <a name="line.1295"></a>
<FONT color="green">1296</FONT>        }<a name="line.1296"></a>
<FONT color="green">1297</FONT>    <a name="line.1297"></a>
<FONT color="green">1298</FONT>        /**<a name="line.1298"></a>
<FONT color="green">1299</FONT>         * Get a string representation for this matrix.<a name="line.1299"></a>
<FONT color="green">1300</FONT>         * @return a string representation for this matrix<a name="line.1300"></a>
<FONT color="green">1301</FONT>         */<a name="line.1301"></a>
<FONT color="green">1302</FONT>        @Override<a name="line.1302"></a>
<FONT color="green">1303</FONT>        public String toString() {<a name="line.1303"></a>
<FONT color="green">1304</FONT>            StringBuilder res = new StringBuilder();<a name="line.1304"></a>
<FONT color="green">1305</FONT>            res.append("BigMatrixImpl{");<a name="line.1305"></a>
<FONT color="green">1306</FONT>            if (data != null) {<a name="line.1306"></a>
<FONT color="green">1307</FONT>                for (int i = 0; i &lt; data.length; i++) {<a name="line.1307"></a>
<FONT color="green">1308</FONT>                    if (i &gt; 0) {<a name="line.1308"></a>
<FONT color="green">1309</FONT>                        res.append(",");<a name="line.1309"></a>
<FONT color="green">1310</FONT>                    }<a name="line.1310"></a>
<FONT color="green">1311</FONT>                    res.append("{");<a name="line.1311"></a>
<FONT color="green">1312</FONT>                    for (int j = 0; j &lt; data[0].length; j++) {<a name="line.1312"></a>
<FONT color="green">1313</FONT>                        if (j &gt; 0) {<a name="line.1313"></a>
<FONT color="green">1314</FONT>                            res.append(",");<a name="line.1314"></a>
<FONT color="green">1315</FONT>                        }<a name="line.1315"></a>
<FONT color="green">1316</FONT>                        res.append(data[i][j]);<a name="line.1316"></a>
<FONT color="green">1317</FONT>                    }<a name="line.1317"></a>
<FONT color="green">1318</FONT>                    res.append("}");<a name="line.1318"></a>
<FONT color="green">1319</FONT>                }<a name="line.1319"></a>
<FONT color="green">1320</FONT>            }<a name="line.1320"></a>
<FONT color="green">1321</FONT>            res.append("}");<a name="line.1321"></a>
<FONT color="green">1322</FONT>            return res.toString();<a name="line.1322"></a>
<FONT color="green">1323</FONT>        }<a name="line.1323"></a>
<FONT color="green">1324</FONT>    <a name="line.1324"></a>
<FONT color="green">1325</FONT>        /**<a name="line.1325"></a>
<FONT color="green">1326</FONT>         * Returns true iff &lt;code&gt;object&lt;/code&gt; is a<a name="line.1326"></a>
<FONT color="green">1327</FONT>         * &lt;code&gt;BigMatrixImpl&lt;/code&gt; instance with the same dimensions as this<a name="line.1327"></a>
<FONT color="green">1328</FONT>         * and all corresponding matrix entries are equal.  BigDecimal.equals<a name="line.1328"></a>
<FONT color="green">1329</FONT>         * is used to compare corresponding entries.<a name="line.1329"></a>
<FONT color="green">1330</FONT>         *<a name="line.1330"></a>
<FONT color="green">1331</FONT>         * @param object the object to test equality against.<a name="line.1331"></a>
<FONT color="green">1332</FONT>         * @return true if object equals this<a name="line.1332"></a>
<FONT color="green">1333</FONT>         */<a name="line.1333"></a>
<FONT color="green">1334</FONT>        @Override<a name="line.1334"></a>
<FONT color="green">1335</FONT>        public boolean equals(Object object) {<a name="line.1335"></a>
<FONT color="green">1336</FONT>            if (object == this ) {<a name="line.1336"></a>
<FONT color="green">1337</FONT>                return true;<a name="line.1337"></a>
<FONT color="green">1338</FONT>            }<a name="line.1338"></a>
<FONT color="green">1339</FONT>            if (object instanceof BigMatrixImpl == false) {<a name="line.1339"></a>
<FONT color="green">1340</FONT>                return false;<a name="line.1340"></a>
<FONT color="green">1341</FONT>            }<a name="line.1341"></a>
<FONT color="green">1342</FONT>            final BigMatrix m = (BigMatrix) object;<a name="line.1342"></a>
<FONT color="green">1343</FONT>            final int nRows = getRowDimension();<a name="line.1343"></a>
<FONT color="green">1344</FONT>            final int nCols = getColumnDimension();<a name="line.1344"></a>
<FONT color="green">1345</FONT>            if (m.getColumnDimension() != nCols || m.getRowDimension() != nRows) {<a name="line.1345"></a>
<FONT color="green">1346</FONT>                return false;<a name="line.1346"></a>
<FONT color="green">1347</FONT>            }<a name="line.1347"></a>
<FONT color="green">1348</FONT>            for (int row = 0; row &lt; nRows; row++) {<a name="line.1348"></a>
<FONT color="green">1349</FONT>                final BigDecimal[] dataRow = data[row];<a name="line.1349"></a>
<FONT color="green">1350</FONT>                for (int col = 0; col &lt; nCols; col++) {<a name="line.1350"></a>
<FONT color="green">1351</FONT>                    if (!dataRow[col].equals(m.getEntry(row, col))) {<a name="line.1351"></a>
<FONT color="green">1352</FONT>                        return false;<a name="line.1352"></a>
<FONT color="green">1353</FONT>                    }<a name="line.1353"></a>
<FONT color="green">1354</FONT>                }<a name="line.1354"></a>
<FONT color="green">1355</FONT>            }<a name="line.1355"></a>
<FONT color="green">1356</FONT>            return true;<a name="line.1356"></a>
<FONT color="green">1357</FONT>        }<a name="line.1357"></a>
<FONT color="green">1358</FONT>    <a name="line.1358"></a>
<FONT color="green">1359</FONT>        /**<a name="line.1359"></a>
<FONT color="green">1360</FONT>         * Computes a hashcode for the matrix.<a name="line.1360"></a>
<FONT color="green">1361</FONT>         *<a name="line.1361"></a>
<FONT color="green">1362</FONT>         * @return hashcode for matrix<a name="line.1362"></a>
<FONT color="green">1363</FONT>         */<a name="line.1363"></a>
<FONT color="green">1364</FONT>        @Override<a name="line.1364"></a>
<FONT color="green">1365</FONT>        public int hashCode() {<a name="line.1365"></a>
<FONT color="green">1366</FONT>            int ret = 7;<a name="line.1366"></a>
<FONT color="green">1367</FONT>            final int nRows = getRowDimension();<a name="line.1367"></a>
<FONT color="green">1368</FONT>            final int nCols = getColumnDimension();<a name="line.1368"></a>
<FONT color="green">1369</FONT>            ret = ret * 31 + nRows;<a name="line.1369"></a>
<FONT color="green">1370</FONT>            ret = ret * 31 + nCols;<a name="line.1370"></a>
<FONT color="green">1371</FONT>            for (int row = 0; row &lt; nRows; row++) {<a name="line.1371"></a>
<FONT color="green">1372</FONT>                final BigDecimal[] dataRow = data[row];<a name="line.1372"></a>
<FONT color="green">1373</FONT>                for (int col = 0; col &lt; nCols; col++) {<a name="line.1373"></a>
<FONT color="green">1374</FONT>                    ret = ret * 31 + (11 * (row+1) + 17 * (col+1)) *<a name="line.1374"></a>
<FONT color="green">1375</FONT>                    dataRow[col].hashCode();<a name="line.1375"></a>
<FONT color="green">1376</FONT>                }<a name="line.1376"></a>
<FONT color="green">1377</FONT>            }<a name="line.1377"></a>
<FONT color="green">1378</FONT>            return ret;<a name="line.1378"></a>
<FONT color="green">1379</FONT>        }<a name="line.1379"></a>
<FONT color="green">1380</FONT>    <a name="line.1380"></a>
<FONT color="green">1381</FONT>        //------------------------ Protected methods<a name="line.1381"></a>
<FONT color="green">1382</FONT>    <a name="line.1382"></a>
<FONT color="green">1383</FONT>        /**<a name="line.1383"></a>
<FONT color="green">1384</FONT>         *  Returns the LU decomposition as a BigMatrix.<a name="line.1384"></a>
<FONT color="green">1385</FONT>         *  Returns a fresh copy of the cached LU matrix if this has been computed;<a name="line.1385"></a>
<FONT color="green">1386</FONT>         *  otherwise the composition is computed and cached for use by other methods.<a name="line.1386"></a>
<FONT color="green">1387</FONT>         *  Since a copy is returned in either case, changes to the returned matrix do not<a name="line.1387"></a>
<FONT color="green">1388</FONT>         *  affect the LU decomposition property.<a name="line.1388"></a>
<FONT color="green">1389</FONT>         * &lt;p&gt;<a name="line.1389"></a>
<FONT color="green">1390</FONT>         * The matrix returned is a compact representation of the LU decomposition.<a name="line.1390"></a>
<FONT color="green">1391</FONT>         * Elements below the main diagonal correspond to entries of the "L" matrix;<a name="line.1391"></a>
<FONT color="green">1392</FONT>         * elements on and above the main diagonal correspond to entries of the "U"<a name="line.1392"></a>
<FONT color="green">1393</FONT>         * matrix.&lt;/p&gt;<a name="line.1393"></a>
<FONT color="green">1394</FONT>         * &lt;p&gt;<a name="line.1394"></a>
<FONT color="green">1395</FONT>         * Example: &lt;pre&gt;<a name="line.1395"></a>
<FONT color="green">1396</FONT>         *<a name="line.1396"></a>
<FONT color="green">1397</FONT>         *     Returned matrix                L                  U<a name="line.1397"></a>
<FONT color="green">1398</FONT>         *         2  3  1                   1  0  0            2  3  1<a name="line.1398"></a>
<FONT color="green">1399</FONT>         *         5  4  6                   5  1  0            0  4  6<a name="line.1399"></a>
<FONT color="green">1400</FONT>         *         1  7  8                   1  7  1            0  0  8<a name="line.1400"></a>
<FONT color="green">1401</FONT>         * &lt;/pre&gt;<a name="line.1401"></a>
<FONT color="green">1402</FONT>         *<a name="line.1402"></a>
<FONT color="green">1403</FONT>         * The L and U matrices satisfy the matrix equation LU = permuteRows(this), &lt;br&gt;<a name="line.1403"></a>
<FONT color="green">1404</FONT>         *  where permuteRows reorders the rows of the matrix to follow the order determined<a name="line.1404"></a>
<FONT color="green">1405</FONT>         *  by the &lt;a href=#getPermutation()&gt;permutation&lt;/a&gt; property.&lt;/p&gt;<a name="line.1405"></a>
<FONT color="green">1406</FONT>         *<a name="line.1406"></a>
<FONT color="green">1407</FONT>         * @return LU decomposition matrix<a name="line.1407"></a>
<FONT color="green">1408</FONT>         * @throws InvalidMatrixException if the matrix is non-square or singular.<a name="line.1408"></a>
<FONT color="green">1409</FONT>         */<a name="line.1409"></a>
<FONT color="green">1410</FONT>        protected BigMatrix getLUMatrix() throws InvalidMatrixException {<a name="line.1410"></a>
<FONT color="green">1411</FONT>            if (lu == null) {<a name="line.1411"></a>
<FONT color="green">1412</FONT>                luDecompose();<a name="line.1412"></a>
<FONT color="green">1413</FONT>            }<a name="line.1413"></a>
<FONT color="green">1414</FONT>            return new BigMatrixImpl(lu);<a name="line.1414"></a>
<FONT color="green">1415</FONT>        }<a name="line.1415"></a>
<FONT color="green">1416</FONT>    <a name="line.1416"></a>
<FONT color="green">1417</FONT>        /**<a name="line.1417"></a>
<FONT color="green">1418</FONT>         * Returns the permutation associated with the lu decomposition.<a name="line.1418"></a>
<FONT color="green">1419</FONT>         * The entries of the array represent a permutation of the numbers 0, ... , nRows - 1.<a name="line.1419"></a>
<FONT color="green">1420</FONT>         * &lt;p&gt;<a name="line.1420"></a>
<FONT color="green">1421</FONT>         * Example:<a name="line.1421"></a>
<FONT color="green">1422</FONT>         * permutation = [1, 2, 0] means current 2nd row is first, current third row is second<a name="line.1422"></a>
<FONT color="green">1423</FONT>         * and current first row is last.&lt;/p&gt;<a name="line.1423"></a>
<FONT color="green">1424</FONT>         * &lt;p&gt;<a name="line.1424"></a>
<FONT color="green">1425</FONT>         * Returns a fresh copy of the array.&lt;/p&gt;<a name="line.1425"></a>
<FONT color="green">1426</FONT>         *<a name="line.1426"></a>
<FONT color="green">1427</FONT>         * @return the permutation<a name="line.1427"></a>
<FONT color="green">1428</FONT>         */<a name="line.1428"></a>
<FONT color="green">1429</FONT>        protected int[] getPermutation() {<a name="line.1429"></a>
<FONT color="green">1430</FONT>            final int[] out = new int[permutation.length];<a name="line.1430"></a>
<FONT color="green">1431</FONT>            System.arraycopy(permutation, 0, out, 0, permutation.length);<a name="line.1431"></a>
<FONT color="green">1432</FONT>            return out;<a name="line.1432"></a>
<FONT color="green">1433</FONT>        }<a name="line.1433"></a>
<FONT color="green">1434</FONT>    <a name="line.1434"></a>
<FONT color="green">1435</FONT>        //------------------------ Private methods<a name="line.1435"></a>
<FONT color="green">1436</FONT>    <a name="line.1436"></a>
<FONT color="green">1437</FONT>        /**<a name="line.1437"></a>
<FONT color="green">1438</FONT>         * Returns a fresh copy of the underlying data array.<a name="line.1438"></a>
<FONT color="green">1439</FONT>         *<a name="line.1439"></a>
<FONT color="green">1440</FONT>         * @return a copy of the underlying data array.<a name="line.1440"></a>
<FONT color="green">1441</FONT>         */<a name="line.1441"></a>
<FONT color="green">1442</FONT>        private BigDecimal[][] copyOut() {<a name="line.1442"></a>
<FONT color="green">1443</FONT>            final int nRows = this.getRowDimension();<a name="line.1443"></a>
<FONT color="green">1444</FONT>            final BigDecimal[][] out = new BigDecimal[nRows][this.getColumnDimension()];<a name="line.1444"></a>
<FONT color="green">1445</FONT>            // can't copy 2-d array in one shot, otherwise get row references<a name="line.1445"></a>
<FONT color="green">1446</FONT>            for (int i = 0; i &lt; nRows; i++) {<a name="line.1446"></a>
<FONT color="green">1447</FONT>                System.arraycopy(data[i], 0, out[i], 0, data[i].length);<a name="line.1447"></a>
<FONT color="green">1448</FONT>            }<a name="line.1448"></a>
<FONT color="green">1449</FONT>            return out;<a name="line.1449"></a>
<FONT color="green">1450</FONT>        }<a name="line.1450"></a>
<FONT color="green">1451</FONT>    <a name="line.1451"></a>
<FONT color="green">1452</FONT>        /**<a name="line.1452"></a>
<FONT color="green">1453</FONT>         * Replaces data with a fresh copy of the input array.<a name="line.1453"></a>
<FONT color="green">1454</FONT>         * &lt;p&gt;<a name="line.1454"></a>
<FONT color="green">1455</FONT>         * Verifies that the input array is rectangular and non-empty.&lt;/p&gt;<a name="line.1455"></a>
<FONT color="green">1456</FONT>         *<a name="line.1456"></a>
<FONT color="green">1457</FONT>         * @param in data to copy in<a name="line.1457"></a>
<FONT color="green">1458</FONT>         * @throws IllegalArgumentException if input array is emtpy or not<a name="line.1458"></a>
<FONT color="green">1459</FONT>         *    rectangular<a name="line.1459"></a>
<FONT color="green">1460</FONT>         * @throws NullPointerException if input array is null<a name="line.1460"></a>
<FONT color="green">1461</FONT>         */<a name="line.1461"></a>
<FONT color="green">1462</FONT>        private void copyIn(BigDecimal[][] in) {<a name="line.1462"></a>
<FONT color="green">1463</FONT>            setSubMatrix(in,0,0);<a name="line.1463"></a>
<FONT color="green">1464</FONT>        }<a name="line.1464"></a>
<FONT color="green">1465</FONT>    <a name="line.1465"></a>
<FONT color="green">1466</FONT>        /**<a name="line.1466"></a>
<FONT color="green">1467</FONT>         * Replaces data with a fresh copy of the input array.<a name="line.1467"></a>
<FONT color="green">1468</FONT>         *<a name="line.1468"></a>
<FONT color="green">1469</FONT>         * @param in data to copy in<a name="line.1469"></a>
<FONT color="green">1470</FONT>         */<a name="line.1470"></a>
<FONT color="green">1471</FONT>        private void copyIn(double[][] in) {<a name="line.1471"></a>
<FONT color="green">1472</FONT>            final int nRows = in.length;<a name="line.1472"></a>
<FONT color="green">1473</FONT>            final int nCols = in[0].length;<a name="line.1473"></a>
<FONT color="green">1474</FONT>            data = new BigDecimal[nRows][nCols];<a name="line.1474"></a>
<FONT color="green">1475</FONT>            for (int i = 0; i &lt; nRows; i++) {<a name="line.1475"></a>
<FONT color="green">1476</FONT>                final BigDecimal[] dataI = data[i];<a name="line.1476"></a>
<FONT color="green">1477</FONT>                final double[] inI = in[i];<a name="line.1477"></a>
<FONT color="green">1478</FONT>                for (int j = 0; j &lt; nCols; j++) {<a name="line.1478"></a>
<FONT color="green">1479</FONT>                    dataI[j] = new BigDecimal(inI[j]);<a name="line.1479"></a>
<FONT color="green">1480</FONT>                }<a name="line.1480"></a>
<FONT color="green">1481</FONT>            }<a name="line.1481"></a>
<FONT color="green">1482</FONT>            lu = null;<a name="line.1482"></a>
<FONT color="green">1483</FONT>        }<a name="line.1483"></a>
<FONT color="green">1484</FONT>    <a name="line.1484"></a>
<FONT color="green">1485</FONT>        /**<a name="line.1485"></a>
<FONT color="green">1486</FONT>         * Replaces data with BigDecimals represented by the strings in the input<a name="line.1486"></a>
<FONT color="green">1487</FONT>         * array.<a name="line.1487"></a>
<FONT color="green">1488</FONT>         *<a name="line.1488"></a>
<FONT color="green">1489</FONT>         * @param in data to copy in<a name="line.1489"></a>
<FONT color="green">1490</FONT>         */<a name="line.1490"></a>
<FONT color="green">1491</FONT>        private void copyIn(String[][] in) {<a name="line.1491"></a>
<FONT color="green">1492</FONT>            final int nRows = in.length;<a name="line.1492"></a>
<FONT color="green">1493</FONT>            final int nCols = in[0].length;<a name="line.1493"></a>
<FONT color="green">1494</FONT>            data = new BigDecimal[nRows][nCols];<a name="line.1494"></a>
<FONT color="green">1495</FONT>            for (int i = 0; i &lt; nRows; i++) {<a name="line.1495"></a>
<FONT color="green">1496</FONT>                final BigDecimal[] dataI = data[i];<a name="line.1496"></a>
<FONT color="green">1497</FONT>                final String[] inI = in[i];<a name="line.1497"></a>
<FONT color="green">1498</FONT>                for (int j = 0; j &lt; nCols; j++) {<a name="line.1498"></a>
<FONT color="green">1499</FONT>                    dataI[j] = new BigDecimal(inI[j]);<a name="line.1499"></a>
<FONT color="green">1500</FONT>                }<a name="line.1500"></a>
<FONT color="green">1501</FONT>            }<a name="line.1501"></a>
<FONT color="green">1502</FONT>            lu = null;<a name="line.1502"></a>
<FONT color="green">1503</FONT>        }<a name="line.1503"></a>
<FONT color="green">1504</FONT>    <a name="line.1504"></a>
<FONT color="green">1505</FONT>    }<a name="line.1505"></a>




























































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